The rice absolutely has to be precooked – where else is it going to get enough liquid to cook? Certainly not from your pepper.
The jury is still out on the meat. We looked at about a dozen recipes for stuffed peppers. Most want you to cook the meat in advance. The couple that let you cook the meat inside the pepper were from older books. So we’re assuming that modern-day sentiments about ground meat being cooked well done is the reason most recipes command you to cook the stuffing in advance. If you cook the meat in the pepper, you should use a thermometer to verify that it has been cooked through. The US Department of Agriculture says it should reach a temperature of 160°F (71°C) to be safe.
Another thing you want to think about, though, is where does the fat go? If you cook the meat in advance, you can leave most of the fat in the pan. If it cooks in the pepper alongside the other ingredients in the stuffing, it’s going to stay right there. One recipe we saw, that stuffs a pepper only with sausage, asks you to poke a few holes in the bottom and sides of the pepper to allow the fat to drain out. But if there are other ingredients – especially spongy little grains of rice – you’ll retain more fat than you’d like unless you use super-low-fat meat, which probably has no flavor anyway.
So realistically, the jury’s verdict is to precook, then stuff. Do yourself a favor, though, and don’t cook the meat to death before you bake it some more. Get it mostly done, lose most of the fat, and let it finish in the oven. And while we’re on the subject, you generally blanch the pepper in boiling water for five minutes before stuffing, as well.