It is possible for a breeder to breed for better health, but it is NOT easy. It is one of the hardest tasks of being a good breeder. The reason for this is health is not strictly genetic, it is affected by BOTH genetics AND environment, separately and as interactions with each other. In order to accomplish better health, the breeder must first control the environment in which their rats are raised. While a breeder cannot control the environment of those rats taken to other homes, which must be taken into account with health records (does NOT mean those records should be discarded, but a breeder has to look more closely and carefully for trends), a breeder CAN control their own environment. This means good nutrition (best nutrition the breeder can provide), proper bedding, clean cages, enough room in each cage, plenty of exercise and mental, emotional, and physical stimulation, highest quality medical care, good air quality, appropriate environmental temperature and humidity, and so on. If one of these isn't right, health can and will be affected. In my honest opinion, cost should NOT be a factor either. If its too expensive, that person should not be breeding. Doesn't mean you necessarily have to be "rich" to be a breeder, but you SHOULD have a steady, stable income and know how to budget properly in order to afford the high quality care for those animals.
Once the breeder has taken care of environmental health, they can tackle genetic health. This is the hard part. A breeder who breeds for better health, has to work backwards, so to speak. You can't just breed two rats together and automatically know the babies are going to be healthy. Ideally health issues will not happen until long AFTER those rats are bred, so you really do not know what to expect until the babies are already on the ground. This is where good record keeping is extremely important. Good, detailed record keeping means you know what to expect and what you need to work with. Just because a health issue does turn up, does not mean the entire line has to be scrapped, it DOES mean some very serious decisions might need to be made. First, you need to know WHERE that health issue came from. If the rats are extremely outcrossed, you will never know, and the issue could very well be spread throughout the entire "line" (making it very hard, if not impossible, to breed out). If the rats are linebred and/or inbred, you can better determine where the issue came from, if you know how to make the right crosses (this is where research and good genetic knowledge come in handy). Once you know where the issue came from, you have to decide if it is worthwhile to continue breeding those rats, and how to go about doing it in such a way the issue will be eliminated, or if you should avoid using those rats, and if so which rats are you going to use instead.
When an issue shows up, you also need to determine if it is actually genetic. Not every health issue is genetic or even strongly genetic. There are MANY kinds of tumors, and not all of them have a genetic component. Those that do maybe strongly genetic, or weakly genetic, they may be genetic with strong environmental factors, they may be genetic but sex-influenced (NOT the same as sex-linked). You need to figure out what it is and what to do about it. For this reason, it is really important to seriously consider having biopsies, necropsies, and full lab analysis done to determine WHAT exactly it is (in many cases just looking at the outside or knowing if it is benign or malignant is NOT enough), which will help you determine if it is actually genetic. If an issue does seem to run in the line (this rat got it, the mother got it, mother's father got it, his father had it, his father's mother had it, etc), then there's a good chance it is genetic. If it runs in the direct line and shows itself in every generation, it is probably strongly genetic. If it shows up sporadically in the indirect line (relatives who are not direct ancestors), then it may or may not be genetic, or may be genetic but strongly influenced by environment. If it shows up sporadically in the direct line, it may be genetic but only weakly so, or may not be genetic at all (if a non-genetic health issue continuously shows up - you need to look at your environment and determine what you are doing wrong to fix that). When a genetic issue does rear its ugly head, you need to determine how strongly genetic it is, how much environment affects it, and what to do about it. Some issues ARE serious enough to stop the whole line right then and there. Others you can work with the line to breed it out, BUT you might want to seriously consider keeping all/most of the babies you produce, knowing there ARE going to be some affected rats and it is NOT fair to place those rats, knowingly or otherwise, to adopters, PLUS you want the best records on your animals possible and you can only get those records by keeping and caring for the animals yourself.
Besides keeping records, breeding later helps. The older a rat, the more information you have not only about THAT rat, but its family members as well. A female can safely be bred at 6-8 months for the first time. For many, it is safe to push that back even further to 9 months, 10 months, maybe even up to 12 months. IF the line you are working with has been regularly bred at young ages, I would start only a little bit older (if the females were regularly bred at 4-5 months, start at 6-7 months), and gradually push it back. Don't push it back ever generation, but every couple of generations. So the first 2 or 3 generations you might breed at 6-7 months, then the next 2 or 3 you will breed at 7-8 months, the next 2 or 3 at 8-9 months, and so on. Gradually push it back every few generations. WATCH those rats, determine which ones are maturing slowly. If one rat grows up fast and stops growing at 5 months of age, but another rat grows slowly and doesn't finish growing until 8 months of age, breed the rat that matured at 8 months instead of 5 months. By doing this you can gradually push back maturation, which will also help push back longevity (generally speaking, animals who mature slower, live longer). It is also important to make sure you are present for births. This may not be possible in all cases, but you can set up a live webcam to keep an eye on the girls while you are at work (assuming you work an office job and you have a supervisor who allows you to do so). In my opinion, it is IMPORTANT to be present for ALL births, because you need to know when something goes wrong. It can be a matter of life and death, not just to the babies, but to the mother herself. If you hold a job that is very strict and will NOT let you take time off, will NOT let you watch a webcam, and will NOT let you leave early when the mother is having issues, you might have a problem. You could very easily come home one day from work on her due date and find her dead in a bloody mess. Not to be graphic, but that's the potential reality, ESPECIALLY when working with lineages that were "historically" bred young and you start pushing that breeding age back.
With males, the only danger of waiting longer is fertility. If males in the line were routinely bred at 8 months or younger, start breeding them at 1 year instead. Push it back to 18 months, then eventually you might be able to push it back to 2 years. Like females, don't do it all at once, or you might lose the whole line when that one crucial male turns out to be infertile at 18-24 months of age. Also about breeding males - the temperament of the male should absolutely NOT change after he is bred. If it does, you are looking at not only health issues, but temperament issues as well. Temperament IS genetic. Temperament CAN be improved or regressed through the right or wrong selections. Really, males should have NO problem being separated for a few days or even a week for breeding, and then put back together. Reintroductions should NOT be a lengthy involved process. Ideally, introductions to strangers shouldn't be an involved process either. In my opinion this is related indirectly to health as well. Hormonal, nervous, anxious, aggressive, etc animals ARE more stressed than happy, laid back, easy going animals. Stress DOES affect the immune system, tears it down, makes the animal more susceptible to disease. So by breeding for better tempered animals, not only do you have better pets who get along with eachother better, BUT you will also have healthier animals. It certainly is possible to breed better tempered animals, but like health it can be difficult. You need to KNOW what you are looking at, you need to KNOW how to pick out nature from nurture, you need to KNOW how to make the right selections to breed better tempered animals.
There is so much more that goes into it than this. It is a long, involved, thankless process (NO I mean it, really, it IS a thankless process). If you are seriously considering breeding at ANY time in the future, start your research NOW. Don't just look at the "hows", look at the "whys". And don't just talk to breeders, involve yourself in rescue as well. You need to see the issues out there first hand to know what you are dealing with. Be careful when talking to breeders - find out what kind of breeders they are and whether you agree with their practices or not. Make sure you understand how and why they are making their selections, and make sure those how's and why's make sense. An obvious example: a breeder dealing with good respiratory health but with mammary tumors running in the line shouldn't be trying to breed out tumors by selecting rats with clear lungs; while clear lungs and respiratory health ARE important and SHOULD be part of the selection, it has little to do with the tumors. Be prepared for criticism - you will get a LOT of it. If you want any kind of recognition or thanks, don't bother, you will NEVER get it, or if you do, it will be rare compared to the criticism you get instead. If you are discouraged easily, don't bother, you will see a LOT of failure before you see ANY improvement. If you are impatient, don't bother, progress happens over time, it will be YEARS before you start seeing ANY trends, let alone improvement.