Again, hard to say from across the internet without knowing where you are, but here's my take.
Looks like you could lose the posts on the ends by hanging an LVL to span both doors. Around this part of the world, they used to do (still see it sometimes) the same thing with doubled 2x12, maybe with a sheet of plywood sandwiched in. Tons of glue and screws and it won't move.
The center posts, though, from looking at your roof structure I'm thinking you're stuck with them. You'd need some kind of truss to span that distance and skip the posts, and once you tear that roof off, that project's going to run into money. If the outside wall is solid/intact, you could keep it, but in reality then you'd be rebuilding almost the entire structure and just keeping that one wall, which might be more trouble than it's worth.
My vote, get a floor under it, leave the end and center posts alone, get 3 or 4 rollup doors on it (depending whether you need the drive through to get a vehicle/ tractor/ mower to the back yard) and use it. Maybe spray insulate that ceiling and stick some drywall or siding/ceiling material up there, insulate/drywall all the rest, and you're set.
Get that vegetation cut/pruned/killed back from your side wall, though- that will rot that siding in a hurry.