Don't buy used, maybe under certain circumstances a used laptop is okay.
The more important question is what are you planning on using your computer for? And what is your budget?
This will answer the question on whether or not you want a desktop or a laptop, they are pretty damn different for their functionality.
There really isn't much to look for when buying a "used" computer. You look at the specs, you then look on the market and see what those specifications are worth new now. You add up the total for the new parts of that used computer, and see if you can get a deal for a couple hundred below that since it is used. This isn't like buying a car where you can ask certain questions to see the condition of the computer lol. If it turns on then it works. Whether or not a piece of hardware will crap out of you is a bit of your hands. You could ask the user to run a few software programs to see how if you have any red flags like bad memory, or to see if it overheats easily.
But yea dude technology is one of the fastest growing markets. Shit becomes obsolete in like no time at all, buying used is a very poor choice because of that.