With 10 acres and the photos you posted - I'd get a small farm tractor - something in the 30 hp range - big enough to handle a 6 ft bush-hog and similar size finish mower, as well as disc up a garden spot or drag off tree trunks, etc.
I'll leave the tractor/equipment junkies over at the equipment forum to make definitive recommendations, but I'd say you're gonna need a good chainsaw(get all the safety equipment, too), some quality lopping shears, at least a couple of gallons of Garlon herbicide, a good backpack sprayer, and some Roundup.
You can probably find a nice little used farm tractor and all the equipment for less than you'll pay for a new lawn tractor - and do more with it, as well.

Your 'brambly bushes' are most likely multiflora rose.

Looks like you have a forest of saplings growing in the back. I am able to cut down 3" saplings with my bush-hog, but they look to be bigger than that and a lot to boot!
And a bush-hog will leave a stump. You will have to remove them.

You might ask a local farmer to come over, take a look, and give you their opinion if they can bush-hog the saplings. If they can and are willing, its a lot cheaper to pay someone to do it, than buy the equipment and not really know how to do it.

Then, you can decide after, what you need to maintain the property.

Regarding Roundup. It works better in the fall when the plant is bringing nutrients back down to the roots to overwinter. That is when the roundup gets into the plant the best and has a higher rate of kill.

If you spray the plants in the spring, when it is putting out, growing leaves, (things are moving up from the roots to the leaves )etc., it mostly just knocks it down, you think it is dead, but the plant will usually come back.

If you have a local Extension office, ask someone if they can come out and give you advice on what to do.

M