If you’re on a budget, get a machete and a pair of work gloves. You can get a good one for $22 on amazon. You will be surprised at how effective they are once you get the hang of it. Clear out a little path then you can use your hands to just yank out the smaller weeds/vines. Once you clear out all the really small/light stuff, go back and get the thicker branches. You can pretty quickly cut through 1-2” thick branches. If you have or can borrow a shovel, dig out the roots of the larger weeds and little trees.
Also, get a thickish tarp. Put your pile of weeds and branches on the tarp and it is pretty easy to drag out to bulk pickup or a burn pile. Much easier than trying to bag it or making 100 trips with an armful.
Jungle Master JM-024L Machete, 28-Inch Overall https://www.amazon.com/dp/B00V7RBGBW/ref=cm_sw_r_cp_api_glt_fabc_766S8HJS9HQ6W0WEE03E