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that turning on a dime, and working in small places = a skid steer. think multi purpose tractor in a zero turn mower form.
fork lifts can also be used. they make attachments for them... pop the forks off, and attach a bucket for example.
telehandler another option.
power-trac = tractor but everything fits on the front.
then ya have a regular tractor.
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i would say focus on maneuverability if it is critical, then that going to limit ya from above options.
then 1 ton lifting capacity,
snow plowing may come down to eating the cash for a plow blade or paying for a higher cost snow blower attachment.
the dirt moving could be critical as well. if your setup more like a landscape / greenery place / sand / dirt place. were they have piles ya just run tractor into, and then dump the material into a customers truck bed or like. overall how high you can lift could be critical and how far you need between tractors front end, and side of truck ya dumping into.
--a regular tractor for example. you can let the front wheels drop into mud / slop and still rely on rear wheels to keep ya going so you can reach further back into an area. a skid steer how ever, you may be stuck, not enough reach, not enough ground clearance.
a shuttle shift or HST tractor, or some sort of hydraulic transmission / hydraulic drive/motors most likely what you will want. to allow better overall control.
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going used....
make sure you test drive machine
let machine run for 15 minutes or so at high RPM's (well let it warm up first, then let it run at high RPM's and drive it around some). raise bucket, forks or other stuff on unit, and then turn off machine with stuff up. give it 30 minutes or so and see if anything falls down. ((getting an idea of valves or cylinders are going to need a rebuild)).
check brakes (left and right), check emergency brake, check all the lights, go through all the gears (low, med, high, for example) double check reverse, tread on tires (what is left) tires can be a rather expensive items to replace. more so on 4wd / MFWD tractors. and needing to keep correct ratio between front/backs so ya do not tear up the transmission or drive train. check for oil leaks, etc...see how sloppy FEL (front end loader) 3pt hitch, etc.. (hydrualic stuff) on the machine is. some stuff ya just go up to high RPM's, and quick move levers/joystick and everything just shakes, and/or keeps moving a few more feet before it stops. tell them DO NOT CLEAN THE MACHINE! i rather see dust / grease / grim on machine. than a spotless machine. were i can not see oil leaks, grease marks, etc... i know unit is used and expect some issues, so let me see those issues. ask them were you could run the forks or bucket into some place, and test the power of the machine / traction. at how well it digs, and well it fills the bucket up. clean the spot backup and put it back to how ya find it. (gives ya a little more back dragging, and responsiveness of the unit).
bottom line, get a GPS or smart phone with GPS on it. and find a list of units near ya. and go look at 6 plus units maybe a dozen, and just try them out, and get a feel for what you want. about only way ya going to figure out good vs bad, and what is avilable in your area. some stuff is just plain "destroyed" and should be in the junk yard, while others look and seem brand new (how well they were taken care of and how well they were used). it is part of spending a big chunk of cash, and doing your homework / researching.