The property was abandoned for 40 years and is in major need of attention. There is an old 1800s farmhouse that we will be renovating over the next year +, while the contractor is out there working on the structure, I'd like to put some time into reclaiming the lot.
There are a lot of old-growth trees on the property we'd like to preserve: pawpaw, black walnut, persimmon, trifoliate orange, poplar, boxwoods (40+ feet tall!), dogwoods, redbuds, cedar, and many more I have yet to identify. The ivy and vines are strangling the trees though, and there are a lot of small saplings that should be removed as well. I'd like to cut a few trails through the back of the lot too.
The primary uses for the tractor:
Finish mowing the lawn (less than 1/4 acre) - That isn't much grass and is not a good fit for a tractor mower. Buy a zero turn or riding mower for same cost than a mower deck would cost on tractor, then you got dedicated machine and no hassle of removing and adding deck, plus much better cut quality (zero turn will cut faster, better, and the experience is more enjoyable).
Removing cut trees - You can chainsaw everything in smaller pieces and garden tractor towing a trailer will handle more than small BX bucket.
Removing brush - BX/B can do this with a grapple, however they lack ground clearance and protection to go in woods. Then the question becomes what do you do with it? You can burn it or use a wood chipper, however BX/B lacks PTO power for those.
Cutting trails - You need larger equipment for this (4-10 ton, costing 75-100k++). You can however 'chip away at it' in a smaller tractor, though you'll run into lots of road blocks.
Hauling and spreading gravel for driveway - A truck will deliver gravel and do decent spread dropping it. After that is done, hired help or racking to finish it is your best bet. This wont be a consistent need.
Occasional snow removal (we get a decent snow fall once every 5 years) - Snow removers are available for garden tractors or stand alone units would work as good or possibly better than BX blower. You can only get front mount blowers on tractors with mid PTO.
Hauling and spreading mulch - Mulch is light and BX would do it fine. Normally this is done every year or longer duration, so depending on how much you need, I'd still say wheel barrow it or hire help (surprising how much work 2-3 guys will do in a day). Aside from transport, spreading mulch on the ground/garden is hand work anyway. You'll likely be buying it bagged too, which a garden tractor + cart can be used to move it (or even a pickup truck). Bags + dump is what I'd do unless you actually need a truckload (that's lots of gardens or trees...)
Hualing and spreading compost - Same situation as above, though it is heavier.
Maintaining a vegetable garden - Don't need a tractor for this aside from tilling the ground. All hand work and people have gardens all the time with no tractor.
EDIT: adding photos to help visualize the property. It's hard to capture the extent of it, but there is a full acre of this level of growth...