From my experience: Just grab a wrench and start playing. Cultivate the nice people at your LBS and when you have a question, ask them.

I restored my bike during the winter months, so when I wandered into the bike shop with a confused look on my face they had time to help me.

Yes, 27 inch wheels were still standard in the '80s (don't ask how I know). I'd look any old wheels over Very Carefully. After all, Stuff happens to wheels. (I'm thinking about learning how to build wheels. A project bike is good for that kind of learning.)

It's possible you'll want a new chain. If so, you probably also want a new 10 speed cluster because of tooth wear. On a budget, I think I'd just clean and lube the chain and see how far it gets me. Unless things are really worn, you can ride the bike until the budget allows for a shiny new chain/cluster.

Brake pads are still pretty standard. The specific kind you put on is your choice. The trick is to put them on so they don't squeak. Mine squeak.

As for tools, and their names, I do what my Dad taught me and call all of them "that G%%$ D@**#$ doohicky." It works for me, and Dad was a darned good mechanic.

I have a copy of Zinn and the Art of Road Bike Maintenance. It got me through the changing out cables and a lot of other things. You do need special cutters for cables, so unless you are planning on doing a bunch of bike work, it really is best to go to the LBS and have them cut the cables for you.

Two sites I found for parts that you don't know you need (yet) are:

http://www.loosescrews.com

for small thingamabops, and

http://www.velo-orange.com

for the bigger stuff.

Also,

http://www.parktool.com/blog/repair-help

can be a big help.

Good luck with the restoration. I know I learned more by just getting my hands dirty than I ever learned any other way.