You might at least consider hiring out the initial clearing of your paths. Then you can buy a tractor sized to groom it and maintain it. I have heavily wooded, steep land also. Cost me less than $2k to have a crew cut, not just a path, but an actual a road through it, including all the trees pushed over (so no stumps) and hauled away--all done in one day. Then I refined the grading and keep it maintained myself with my 26HP SCUT. I have no problem cutting smaller trails with my SCUT, or even by hand; I always try to leave the bigger trees and route the paths around them. I tend to leave brush except where I need a path or a view, as it is good for attracting wildlife.
Clearing wooded land is a lot of work for sure. I hate stumps but hate digging them out more. I don't like burning but chipping is a tedious and dangerous job. In fact, tree-work is dangerous on all fronts, especially if you're not experienced. Just maintaining wooded land--removal of dead wood--is a lot of work and is an ongoing job, and very hard on the back. I handle these jobs different ways. The biggest job I hired out completely. Sometimes I hire someone to drop and buck a larger tree then take care of it myself. When I needed a couple dozen "flagpole poplars" gone, I hired them to be hauled away. One time I hired an enormous
chipper that could chip an entire tree in less than a minute + a crew to run it, and got rid of dozens of trees and gave me a nice pile of chips to compost. Cleaning up deadwood "pick-up sticks" I love to hire a couple guys to do that, when I can find them. Dead wood, I collect in a big pile over time, then sometimes burn it, but other times will simply collect the wood in an out-of-the-way location and leave it to decompose, plus that makes good habitat for wildlife. Large dead trees that are not a hazard I try to leave as they attract owls, woodpeckers, and other wildlife.
I have consigned large sections of my woods to nature. I only groom the edges where the woods meets cleared areas, which makes it look nice. Certain other areas where I walk or needed a view, are more intensively maintained.
If you're determined to tame large swathes of your woods and do it all yourself in small bites, everyone here is correct, bigger is better and probably safer.
Just a few thoughts from my experiences with a similar property.