Goats. Theres folks who rent out their goats for this very task.

Either rent a brush hog, pay someone, or a little bit 1 day at a time with hand tools.

I’ve cleared areas like this around my house w/ the battery hedge trimmers and lopper I already have, with a little assist from a chainsaw (for larger limbs) then weed-wacker or lawn mower for final cleanup. OTOH I just paid a guy \(400 cash to come out and clear half an acre w/ a bush hog (which can't deal w/ the larger trees FWIW) so I could get horizontal geothermal installed in an overgrown meadow, and I'm glad I didn't DIY that one. It took the \)100K+ bush hog a few hours to get through it, I’d have died.

Your idea sounds like maximum cost and risk but also maybe the best opportunity to play w/ big dangerous stuff which could be fun.

You can probably hire a landscaper with the right equipment to clear it for you and take it away for the same $2K you would spend on a rental. Buying and then reselling the brush hog might save a little at the price of a lot of work. I would get some quotes to hire out the job before taking it on yourself. My experience with this kind of work is that it is always harder than it looks.

Texas? That brush looks like yaupon, which is a PIA to remove. Cutting it is the easy part, disposing of it the hard part. The tops turn into a rats nest of interlocking branches. I have lots of 20’ tall thickets plus lots of younger growth. I’ve cleared a few acres by hand, mostly with a \(40 6" electric chainsaw. The trunks can be run through a wood chipper (\)500-750), but the tangled ends are difficult. It burns like crazy, so if you have space for a wood burn pile just pile it up and strike a match. Again assuming yaupon, cutting it down only encourages it to grow more. You will need to spray the cut trunks with Round-Up or another similar brush herbicide. Yaupon is difficult to kill and in two months you will likely be cutting the new growth that regenerates from the roots and spraying again. Some areas have taken three passes to (hopefully) eliminate. While you are at it, though, yaupon leaves are good for tea, mildly caffeinated. Deer eat the leaves and berries, bees visit the flowers, so leaving some near the property lines will create a privacy fence while helping the wildlife.

Home Depot rents walk behind brush cutters.

Mini chainsaw. Potentially a regular chainsaw.

Bulldozer. My dad did this to our backyard once. Took a couple of hours and left a level field for new landscaping.

Most efficient-forestry mulcher.

Tons of ways to do it, from some loppers and a trashcan to just paying someone, it all depends on what you’re willing to spend.

I would hire someone to bushhog it. They bring their own equipment and it’s cheap when you consider the amount of labor it will take to do it yourself.

We’re clearing about five acres now

Skidsteer with a hydraulic brush hog. I’ve done this before.

Definitely not with a weed whacker…

Honestly just rent the correct tool and be done with it. Nothing wrong with renting if it is for occasional use.

Goats. Rent some goats and use a simple temp fence to keep them in the area you want to clear.

Get a 15 gal electric tank sprayer and some Crossbow weed and brush killer (or some other named Tryclopyr and 2,4D weed killer combination) and spray it. Give it some time, It will kill the woody and weedy plants leaving behind the grassy plants. Much easier to deal with dead than alive. You will need to do this anyway if you want to maintain it without the need for continual brush hogging.

Why tear up the land? Ruining habitat for lots of animals and insects.