Mini excavator?

[Buckmark]

2500-3000 will buy you some used tracks or a clean out bucket 

[fishngamereaper]

Unless you plan on making money with it don't buy one. Renting is way cheaper. Maintenance costs alone will hurt the wallet.

[Firedogg]

Find a used Case or John Deere backhoe with a thumb. A mini or sub compact anything will leave you frustrated up at a cabin property, especially the first time you need to remove a stump more than 10" across or have some big rocks.

[luckyman]

Pulling levers is the easy part but Unless you've operated equipment before you'll be surprised at how little you get done in a day. You will save a lot of money by hiring it out.
If you just want a cheap junker to mess with and have the time you may find something in real poor condition you can tinker with.

[j_h_nimrod]

It would likely be much more cost effective to hire it out. A good operator can easily get more done in a day than a novice can in a week of Saturdays. Your budget points that direction as well, maintenance and repair can be killer expensive on older machines.

[Jpmiller]

Bobcat tracked loader. You can get grapples, snow blower, stump grinders, augers, ditch witch, soil conditioners, field mowers, and any other attachments you want for it. It's a good way to get a machine and slowly add on for what you need. It doesn't "dig" well but for property maintenance I use it almost daily when I  am helping out my old man at his place and he is in it when it's just him. Way more versatile than an excavator and as long as it has tracks it'll go almost anywhere.

[Wingin it]

That budget won't buy you anything useful at all. You would be money way ahead to pay somebody else that money to perform the work for you. You will be lucky to get more than a day of work, maybe two for that by the time they mobilize a machine and spend some time on it. Hopefully you don't have to export much either because if so you are going to be way over that budget. If you are skilled at something try to work a trade for the work or a portion of it anyway.