Dealer/service available close enough to you.
Parts available? Sometimes a problem for off brand tractors (even if it seems to be the same as another brand, core components can be spec'ed a bit different).
Learning what name each manufacturer calls the same thing (and you thought women's fashions were difficult....).
At least 12 speeds fwd. Lets you choose the right speed, especially for haying.
I would approach this the same way as a pulling/towing truck: pick out the hardest task, and the range of equipment to do it (for example, the bailer), then work back. Let the task determine the tractor.
Do you need a loader? Not if it is a field tractor.
Do you need 4x4 (mfd, etc)? Likely not if all it is doing is haying (it shouldn't be muddy if you are cutting, raking, and baling hay).
Two speed pto? Cheaper for some tasks to run the higher speed unit (maybe mowing?) for easy tasks.
How are you going to move it if you need service or have other places to take it? Might mean a trailer you already have, or one you need to get (and an appropriate truck).
For example, I had an old Case, collected cat 1 implements for the day I bought a newer tractor. Then bought a cat 2 machine. Cat 2 implements are not near as easy to find used (and still have life left in them). Yeap, cheap I am.
As for me, I looked at the established brands, as I knew I was not buying new, and wanted long term support, parts wise. I finally found what I thought I wanted, for the $$$ I was willing to spend. TN-55s. Knowing more (and having more time to dwell on it) I would have bought the TN-60 or higher due to a larger front axle (not that I have made it work enough to matter) and I would have looked for the 12 or 16 gear unit. This line could have what you are looking for.
Another detail: adjustable end links on the 3 point. It is never fun attaching something to it, but that helps. And if a loader is important, one that has a skid steer attachment is sure nice (several folks sell new end links for the FEL if one wants to convert later). Extra hydraulic circuits are a real plus (swinging blades, top and tilt, raise/lower/depth adjustments for drawbar disks/plows, swing away tongue on a small bale baler, etc).
Look into the 'affinity' programs. Those are the discounts a brand will give if you belong to a certain organization. Deere gave pretty large discounts for belonging to the 1/4 horse association when I was looking, but had a limited selection of models (nothing I wanted). Since the recession they have opened the range up quite a bit. For the price of a membership it can be a substantial savings. Ask the salesman. Pre-inventory tax time could work your way too.