It sounds to me like you could skip the backhoe attachment. They are expensive, heavy, and a pain in the 3-point to put on, remove and store when not in use. Having a flat, level paved area to set it on when storing it off the tractor will help, but then that is taking up valuable space while just sitting there gathering dust.
You mentioned "sheep" and feeding hay. The biggest question I have for you is what kind of bales are you going to be working with? Round bales? Square bales, large or small? If your source for hay only comes in large (read *heavy*) round bales, then you are not looking at near big enough tractors to handle moving large round bales. If you're going for small square bales, are you confident you have a reliable source provider for these small square bales? Most Ag's around here don't/won't produce small squares because it's not worth their time. So it's normally large round bales being produced and sold here. The key will be finding a reliable hay producing source that is willing to put up small square bales every year. Do you have a space to put up square bales under cover, out of rain/snow, etc?
For a mower, a belly mower will drastically reduce the amount of ground clearance your tractor has while it's on. Yes they can be taken on and off, but on most designs, it is not super simple or easy. Not near as bad as taking on and off a backhoe, but it may make you not take it off maybe every time you should, or hesitate to put it back on when you kind of need it. And a belly mower won't take much abuse from heavy brush or rocks or other small debris that a true rear mounted brush hog style cutter will breeze over and take in stride.
A brush hog style mower will not give you a park or golf course like cut appearance like a finish mower will. But for pasture work, they are more robust and will take the occasional rock (and brush cutting) in stride where a finish mower may blow it's guts out on you. The cutting blades on a brush cutter spin slower, are larger/thicker/heavier and they are also dull (on purpose) for chopping and hacking, not truly slice cutting the grass like a knife blade.
A finish mower is made for cutting grass, and that's it. They won't tolerate brush cutting for long (or very large brush at all), and they don't take impacts well with uneven ground or rocks and other debris. The blades are smaller, thinner, lighter and they are sharp like a regular lawn mower blade. They do require sharpening from time to time as they dull from normal use. They also spin at a much higher speed. All this is what gives them that park like clean finishing cut, but it does make them much more prone to damage from foreign objects.
Hanging a 3 point hitch style rear mower, either finish or brush, off the back of your tractor will make it hard to maneuver around obstacles, buildings, cars, etc while you're mowing. A belly mower would be easier to mow around obstacles with, but it will still be difficult to get close to walls, sprinklers, flower beds, etc. You'll need some kind of secondary mower for getting around "stuff" in your yard and around the house. Either a push mower, or a riding mower will be needed, as well as some kind of string trimmer/weed eater for getting the last finish work done.
We're just under 4 acres here presently, but I mow about 6 acres (neighbor's pasture too). I mow all the pasture area, road ditches and rough places with the 3 pt rear brush hog mower. And I mow the "lawn" areas around our house and out buildings with a plain old riding lawn mower. I also use a string trimmer around the house, trees, fence and flower beds that are immediately around the house and back yard. I don't worry about trimming around the out buildings, lean to, or pasture fencing.
