Sorry we are rather late to the party, and our a subject we can potentially offer some knowledge on too.
Mowing implements for quadbikes are expensive to buy and run, and can be awkward to maneuver. If mowing is one of your key objectives this immediately rules out the quad option.
The tracked Iseki will also be a poor buy for your purposes. These are available cheaply on low hours because their uses are extremely limited - in Wales only useful job is flail mowing steep and/or wet moorland.
After that, consideration should be given to the size of your site, mechanical understanding and willingness to conduct maintenance yourself.
Be happy to help you think through this some more, but some guidelines might include:
Sub-compact with mid mounted mower, eg Kubota BX series. Excellent for neat mowing, good slope stability, no problems towing trailers or powering hydraulic equipment such as wood splitters. Limited range of machinery possible for rear due to small size. Usually hydrostat so easy to manouver. Competent for loader work. Limited ground clearance can be a problem.
Compact utility tractor, eg Kubota L series. Larger, tougher and more capable but a slightly more heavy duty driving experience than the sub-compact. Big enough to handle some 'full size' implements such as larger flail mowers or a haybob. Can lift a large round bale.
All of the dedicated machinery available to allow compact tractors to undertake proper field work such as balers and drum mowers are mind bendingly expensive to the point where they are mainly limited to the wealthy playing at farming, as any sort of payback time will be inconceivable without a strong contracting market.
Vintage tractor, eg International 275 / Ford 3000. Not to be underestimated, especially if you have a larger space and no need for intensive loader work (where the manual transmissions and steering can become a burden). A much lower purchase price is buying you a 'proper tractor' - which really means it is big enough to borrow and make use of the old implements your farming neighbours all have lying around in the corners of their yards. The downside is their age, it will help if you have the necessary knowledge or help to buy a good one in the first place. A good solid machine will still leave you with half your budget as well as a somewhat appreciating asset.
(Recommend something new enough to have a dual clutch for safety reasons, so sorry no grey fergies
) 4x4 essentially not available.
Classic tractor, eg Ford 3910. Mostly as above, but in return for most of your budget you will get synchromesh, power steering and a strongly appreciating asset. 4x4 will be out of budget range.
I have two machines for sale, neither of which I would expect to meet your needs, but a glance at the classified section may provide food for thought?