There's a BUNCH of different ways you can go about this thing, but one aspect you really should consider is insect damage and if there are still living bugs crawling around in and around it. I kind of doubt you would want a bunch of termites breeding in your living room although that's probably not a serious threat..
We have no idea how much money you have to spend, but it could quickly add up depending on what you are going to do.
If it were me and I wanted to invest in tools and equipment I'd buy stuff I'm going to use and need well after this project is completed on future projects. I'd love to say I've never purchased equipment that I never used again, but I'm fundamentally against lying about things like that..
A decent set of hand planes can be had from places like ebay and not all planes are made alike.
A good Stanley #4 and maybe a #6 might come in darn handy, but go for those made back when real craftsmen made them instead of the stuff popping out of Chinese factories these days.
I mentioned the cheapo plane I turned into a scrub plane, but it was never worth much more than that.
For around $30 you can probably get your hands on a decent plane made somewhere in the 1940s or thereabouts.. EBay is your friend in that department and then you may want to invest in some sharpening equipment or tools. Nothing beats a plane iron you could shave with. (not that I'm suggesting you take up hand plane shaving) Then you can get into whether you want to go with water stones or diamond stones...blah blah blah..
Woodworking is fun and satisfying, but I'm probably not the only one who is going to suggest it's only going to get more expensive and confusing as you go along..
I hope anything I have to add is marginally helpful, but I'm not betting the farm on it..