OK, I see you're a tool guy, too. Seems to make sense, to take on a project like this.
Yes, those vibrating multi-tools are really handy to have, I bought one that works with my Ridgid set. The reason I went with Ridgid is that they have a lifetime warranty on everything, tools, batteries, and chargers. I'm tired of trying to replace the batteries and chargers for otherwise working tools.
For the demolition work I did, a sawzall and small right hand grinder were valuable. There were a lot of pieces that were nailed and stapled where pulling the fastener wasn't possible.
I have a compressor and different nail guns that I use for my work so was lucky there. Almost all of my framing repairs were done with the joints glued with construction adhesive and either nailed or screwed.
Another nice tool to have is an electric stapler. I have two of them, one that shoots a narrow crown staple (used for siding and carpet installs) and one that shoots standard wide crown staples (used for attaching poly vapor barriers and stuff like that).
I'm always of the opinion that a guy can't have too many tools, lol. Hope you get your tool bench filled with your project.:)