Rent the floor sander. You'll leave a wavy surface with a hand sander. Otherwise, it ain't rocket surgery. Sure, there's a small possibility you'll screw it up but it's a small room and you gotta learn some how.
Pull or set any high nails, fill large holes or gaps, light sand, stain (if you wish), seal, light sand, seal, wait, light sand, wait, seal done. I'd pull off the baseboards to prevent them from being dinged and plus you can then sand all the way to the wall and cover the edges when you're done. Might take a weekend on account of the waiting between coats.
You'd need a hand or disc sander for inside of the closet(s) if you have them. You are welcome to borrow my cheap old belt sander if you don't want to buy one, but the floor sander is worth renting I thought. I also have a random orbit sander for the edges and corners if you need it.
You probably don't need to take off much material unless you want zero hint of the current color, so you're really looking for a floor polisher/buffer and not a sander. The first pass is with a mildly aggressive screen at most then the intermediate passes are with fine grit (essentially like a Scotchbrite).
Oh, do start in the middle of the room the first time you turn on the sander so you don't put a hole in a wall... Don't ask.
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