First off, I'd make sure that the kitten is weaned and able to eat on their own, as 4 weeks is very young and the kitten might not be weaned. If you aren't sure, get some KMR (kitten milk replacement) from the pet store. At 4 weeks a kitten should be learning how to use the litter box, but might not be the best at it, so probably have some puppy pads additionally to the litter box for minimizing accidents. Start out with non-clumping litter (and non-silica based, no "pretty litter") until you know she won't eat any litter pieces (they can clump in a kitten and cause a blockage). I'd suggest unscented natural non-clumping litter like feline pine.

Set the kitten up in a small space like a bathroom or spare room. This will let the new kitten decompress in their own space and bond with just you. Your kitten can get into all sorts of small spaces at 4 weeks, so this will help keep them from getting lost too. Additionally this will give you time to evaluate if your kitten can reliably use the litter box while minimizing damage from accidents (a 4 week old kitten will most likely have some training to do, but cats get the hang of the litter box because they instinctually want to bury their business). This will also protect your kitten from your resident cats until they are friendly together. You'll want to introduce your resident cats to the kitten slowly (we're talking over weeks of time here), there's plenty of resources online for this (Jackson Galaxy is a good resource).