What is the best way to cook chicken if I plan on microwaving it a few days later?
Under such tight restrictions, one step that might help is brining. This would apply to chicken breasts, pork loin, or pretty much any other lean meat; darker cuts such as chicken thighs will benefit less, but there's no reason you can't brine those if you want to. 

You can find a quick primer about how and why this works here; in short, brining denatures some of the proteins that "squeeze" moisture out of the meat as it cooks, which reduces moisture loss in the finished product. You don't really need anything other than salt, water, and time, though many recipes will call for additional flavoring agents.

Make sure that you don't overcook to begin with. If you can, get a thermometer and measure the meat's internal temperature. Here is a decent guide to the recommended temperatures for various types of meat; remember that you want to cook to slightly below these temperatures to allow for carryover. 

From personal experience I would advise you to vary your technique and try to cook different variations on the same basic food; this guards against boredom, and makes it easier to stick to a regimen of weekly meal prep. Instead of broiling, cook your chicken on the stove, then make a basic pan sauce to serve over it, which will add moisture and flavor. If chicken thighs are on sale, get some and braise them instead (you don't need to bother with brining if you do this). This takes some time to cook, but it's very easy, and they'll reheat well for days.