I would love some links on where you're doing your research on laser cutters. My wife recently suggested I buy one which is like, oh god how did this happen, I must make this happen as fast as possible before this opportunity goes away!
I kind of just googled around for information; there isn't a whole lot of well-collated stuff, so I definitely could have missed a better option, but it looks like if you're not going to shell out for a very expensive commercial/industrial unit or wait <undefined> months for Glowforge, you're probably looking at a K40. There's a pretty good wiki for it on the lasercutting subreddit: https://www.reddit.com/r/lasercutting/wiki/k40
You'll quickly notice that it's not a terribly good laser cutter, although it does come with the 40W necessary to be one and can be upgraded further. There are a variety of upgrades you'll want, but if your budget is $1K, the laser cutter itself will cost you less than half of that; they run $400-450 on ebay.
So if this were a Top Gear challenge, you're sitting pretty to improve your cheap lemon with your remaining cash:
* The default controller only works with Windows and the software it comes with is likely pirated. If you're used to working with 3D printers, get a RAMPS board and put Marlin or something on it. There are a few guides for going from there to more open control software, or even running off of an SD card with no PC.
* Ventilation. Apparently the stock fan doesn't fit that well, and there's no system to blow debris off of the bed when a cut is in progress. That could be a fire hazard and/or bio hazard since the dust from stuff like acrylic is not good for you.
* Cooling. It's water-cooled, with a small aquarium pump that you stick in a bucket of water. It looks like that's probably fine if you aren't going to run the laser constantly, but you could always get something with more flow.
* Some users say that you should ground the metal housing manually with a thick strand of wire. That's a mildly worrying piece of advice.
So it sounds a little hair-raising, but all in all it seems like a manageable risk, and the price is right.