I've got a Bobcat 630 - late 1970s vintage. Bought it when I was building my workshop with the intent to sell it again when the project was finished. They hold their value, so I figured even if I sold it for a few hundred less I'd still save a bunch on rental fees. It has been so useful that it is still here fourteen years later...
Most of what I've heard regarding the tracked loaders is that they don't do as well in snow as the wheeled loaders. The greater contact patch just doesn't give you the same traction when pushing snow. As you say, they float over the snow rather than chewing down through it. Conversely, they will give you better stability in soft ground conditions.
Watch the slopes with a skidloader. Probably better than a tractor because the center of gravity is lower, but you can get yourself into trouble rolling it forward if you try to dump a bucket load down a slope or lift it too high while traveling. Also, not sure how old your kid is, but make sure he is responsible and understands the operating procedures. I've known of a few grown men killed by them. A semi-common fatality is getting out of the cab with the arms lifted and having them come down for some reason and crush the person.
I've got a 4:1 bucket, snow bucket, and a set of pallet forks for it. Certainly comes in handy for the tasks you've mentioned. Personally, I'm a fan of the Bobcats. I like the hand and foot controls. For me, it is easier to do multiple operations at once with them - move, turn, lift, dump, etc. IIRC, the Gehls are all hand control. Never got adept with that setup. The newer models seem to be going to full joystick control - one side for movement, the other side for the lift arms and bucket. More a matter of trying them out and seeing what feels comfortable for you.
I've been pretty lucky with my skidloader. Other than regular maintenance - fluids, filters, plugs, wires, etc - I've replaced a couple hydraulic lines, rebuilt the carb, and that has been about it. It isn't much to look at, but it keeps plugging away. Conversely, I picked up a Bobcat X320 mini-ex (mid 1990s vintage) the other year for a decent price. I knew it needed some work, but so far I've replaced nearly all of the hydraulic lines and rebuilt a couple hydraulic cylinders. I'm also dealing with some hacked wiring the PO screwed up. I still got a good price on it - several thousand less than what I've seen others going for - but have about $1500 into it in parts and hours of time.
Depending on how much you plan to use the backhoe, take a look at the mini-excavators. Being able to swing 360° and travel makes quite a difference in a lot of projects. I've found the "cat's paw" attachments to be pretty much useless except for the most minor trenching/digging operations. You have to move the whole loader around entirely too much while trying to dig. The ones that swing side to side are a modest improvement, but I still see them all as for someone like a landscaper who does 90% of his work with the loader and only occasionally needs to trench or dig a hole. The full backhoe attachments are better, but have the same issues as a tractor-loader-backhoe (TLB) as far as maneuverability goes.
Like with our Toyotas, first recommendation is to pick up the service and parts manuals. The parts manuals are worth it just for the exploded diagrams. Gives you a pretty clear idea of what you're tearing apart. As you reach the bottom of your price range, I'd want to be comfortable working on it myself. Labor rates at the local dealer can be spendy. At the upper end of your price range, I'd expect to get a pretty clean machine that didn't need much. A lot of people consider the Bobcat 76x and 77x models to be the best Bobcat ever made.
Hope that answers a few questions and feel free to ask more.
