One of the biggest things is to make sure youre getting everything you need. a lot of people and businesses will sell just the drum shells with no hardware included. if this is the case, you just need to make sure you get all the hardware that you would need, such as bass pedal, throne, tom holders, cymbal stands, snare stand, sticks etc.
also, youre probably going to need new heads once you get the set whether its new or used. stock heads are generally very poor quality, and if youre buying used, its always a good idea to put some fresh heads on.
look at the wood type also. poplar and basswood are generally the cheapest(200-700$), with maple and bubinga being the most expensive($1000+). birch is in between, as are mixed plies. if buying online, expect shipping to be 150-200 bucks.
Take a look at mapex, tama, yamaha, pearl are all good brands. sonar, sound percussion, and ludwig are cheaper brands more aimed at beginners.
Those are my general tips. feel free to email if you have more questions!