Sorry, I forgot to mention that I already have some Shimano downtube cable stops, since I had planned on upgrading to Tourney shifters before I noticed the incorrect rear wheel.
It sounds like shifters and cassette are the only real necessities unless I run into problems after installing? I can get Tiagra 4700 shifters and cassette from ebay for fairly cheap, and a new rear wheel is about $80 from what I see online. The current wheel is 126mm 7-cog hyperglide so I can probably sell it and recoup some losses. This really wouldn't be too bad for a bike that I got off craigslist for $100. I love how gorgeous this frame looks, so I'm willing to go through some extra work for it. I know a new bike would be lighter and automatically come with the better gear, but I like projects like this and it's a great learning experience for bike maintenance and repair.