Here's how you'd rank the Ski Doo engines in your budget range:
(1) 600 non HO, or 500ss, same thing depending on the year. Bullet proof.
(2) 600 SDI.
(3) 600 HO
The 600 HO, at least in 03 and 04, had some bad rings, but they've been replaced if the sled is still running (likely). I've got an 03 in the garage with around 12,000 miles on it. Rings were replaced under warranty first year, and did a top end at 7000 miles.
The carbed 600 (500ss), and the 600 SDI are solid. I've had them both in the 6-7000 mile range before selling, and my brother currently has both that are North of 10,000 miles and never been touched.
I'd for sure pick the 600 carb'd first though, when buying used. You can find a low mileage, clean unit for around $2,000 and you'll probably never wear it out. Like this one.
https://appleton.craigslist.org/snw/d/2002-ski-doo-mxz-600/6719416159.html