Don’t even think of burning the poison ivy. Put some body oil on your skin, put on long sleeve protective clothing, glasses and gloves (if you are allergic to poison ivy) and gather those vines by hand, bag them up. You can shred the rest in a chipper shredder. Wood that works for mulch can be chipped in one pile, leaf and twigs shredded into a compost pile.
I always found it easiest to clear out all vines and undergrowth, remove those. Then you can better see which tree branches you want/need to get out of the way to make room for bibber cuts, and direct your shaded/sunny areas. Be organized in your work, clear and clean so you don’t have trip hazards and housing for potential unwanted animals.
Be cautious around brush and piles sinc3 both poisonous and non poisonous critters like to take shelter in them. Do a little at a time. Use logic.
“if you are allergic to poison ivy”
and if you are not YET allergic to poison ivy/oak/sumac, you WILL be allergic after the 3rd exposure, because almost everyone is allergic by the 3rd exposure ...