Do you mind if I ask how much you paid for it?  To answer your question that if you are middle aged like I am you would want something with power steering and convenient to operate.  Further, cost of the tractor would be critical so it would be expensive to hang that 237 on a 630 or 730.  I would look for a 3010 or 3020 diesel.  You should have the screens already for either of those two.  An A or 60 would be cheaper to buy but then you have to go get screens if you are going to run with it.   I saw a very usable but not pretty 3010 diesel sell a couple of years ago for 2,700 dollars at auction.

I am new here, and I have never mounted or moved a mounted picker but I have loaded and moved a lot of old farm equipment. Obviously if you can get the A ready and have all the mounts and all, and you don't mind working in someone else's shop or yard, then  you could haul A mount picker and drive on trailer then haul home. Plan B, I've used this one and plan C on a few odd sized things with no wheels; if you have enough room in the budget to hire a roll back truck, take two 4x6's long enough to go past the picker front to back let's say it's 14', turn them up on edge and cut both ends rounded like a sled runner, I just use a chain saw, it doesn't have to be fancy, then bring like six or so 2x6's 8 foot long, a digging bar or big pry bar, a bunch of thick wood blocks / cribbing, 4 big eye bolts 2 heavy ratchet straps, hammer and nails, cordless drill, drill bit the size and length of the eye bolts, three inch deck screws, and some kind of no electric saw, I usually use a chain saw. Use digging iron and a block to lever up and get enough locks or cribbing under it to get your jack under, then just work your way around jacking and blocking until you get it about 9or so inches off the ground. Place your 4x6 sled runners up on edge front to back under the picker or just to the outside edges then lay 2x6's as cross members underneath flat, front back and mid points, screw them to the top edge of the 4x6's then use the other 2x6's the same way doubling up your cross members like a laminate board, so they can take the weight of the picker. Screw them together with 3" screws, so now basically you have built a big heavy duty pallet in place under the picker with the bottom edges shaped like a sled, make sure the "pallet" is narrower than the length between the width of the rollback if it has the bed rails on it. ( I usually go measure the truck the company is going to use. ) trim off the extra width of the cross members with chainsaw or cordless saw, then drill holes in the four corners of the pallet skid and put the eye bolts in. Next let the picker down on your homemade skid pallet and strap the picker to the skid using the eye bolts to hold you ratchet strap hooks. Hook a chain or cable around the doubled up 2x6 on each front corner so when taught it looks like a triangle. Call the rollback he can winch it rite up like they do those Amish sheds on skids, and away you go. It should slide rite off when you get home. Sounds like a lot but it usually shouldn't take more than an hour or two. 

Plan c: if no rollback follow all the above but bring 2 coma longs and some chain, cut some schedule 40 plastic pipe, or steel pipe into pieces about 2feet long  cut at least 6, 8 is better, put a piece under each sled runner and use them as rollers while you com along the thing up the trailer ramps adding as you go then taking off the back and adding back to the front. "Like an Egyptian railroad" this works very well just takes a little more time and effort then the rollback. hope I didn't confuse you and this helps.

Adam