The specks of rust on the frame are minimal and of no concern. I call it patina . . . The cosmetics look pretty good. I would strip all the components off the frame and give the frame a good cleaning, being careful of the paint and decals. It will look just fine.
As for components, are you planning to keep the same or similar components, or are you planning to change most of it out? If the latter, I'd trawl eBay for complete used groupsets, they show up often. Even if you don't end up using something, e.g. the brakes or the headset, it is less expensive than buying each piece individually. Also watch Craigslist for donor bikes. You can spread the frame if needed to accomodate a wider rear hub. Something like 7 or 8 speed would be nice.
There seem to be a few bike coops in Houston. Worth a visit to root through their parts bins and ask about classes. New budget wheels look odd on vintage frames in my opinion, the blocky modern hubs and squared off QR levers just clash with the bike. Used wheels are spendy to buy on eBay due to shipping costs. A used wheelset from a coop might be the answer, or for more fun, build up a wheelset using the existing hubs but new alloy rims.