Can a tractor do it? Yes.
Should you bother buying one for such few tasks, mostly seasonal? Only if you want something else to maintain.
You only reclaim your property one. After that, it's just maintenance. It would probably be more cost effective to hire someone for the brush cutting.
As for your other tasks, you're looking at a couple hundred for a good used rear tine tiller, a lawnmower, and a cheap driveway conditioner to pull behind the mower. I can't imagine the total being more than $3-4000 for the above, not including paying someone to clear the brush.
No more than you have there, a BobCat mounted brush mower could have cleared off in less than a day. At the industry average of $50hr (don't know about your specific market), that's probably less than $500 and no headache for you.
If you're dead set on owning a tractor while knowing nothing about them... I'd suggest talking with your local dealers about what's in your price range and try them out. Don't get caught up in the brand game. When you're buying used, you're buying what works for you without a warranty... and that's not a brand, it's a preference.