I was given an old (basically unused) Bridgestone Kabuki Skyway 12. I want to restore/upgrade it to use as my commuter. It's an old road bike with 27x1.25 tires, a thread on 6 speed freewheel, Suntour Vx derailleur, stem friction shifters, suicide brakes. There is a world where I would love to put some STI shifters on it, but in the world I live in, I do not have a fountain of money in my back yard.

Here are a link to bike pictures.
http://imgur.com/a/9mOPr

What I want to do is move to 700c tires, upgraded brake levers, indexed rear shifting, and I might as well move to a 7 speed freewheel while I'm at it.

I have done as much learning as I can, and here is the equipment list I have so far:

Tektro RL340 Brake Levers
Wheelmaster Weinmann LP18 Wheelset
Shimano Tourney Freewheel (I would like to do the 14-34T, but I will stick with the 14-28T if 34 is too big)
Shimano A050 Thumb Shifters

Any red flags? Obvious incompatibilities? Recommendations of better gear in the price range? I've done some reading, and I think I'm okay, but not sure. I also don't know if I will have to replace the rear derailleur or not.

Thanks in advance for any help/advice/smackdown.