You can almost certainly rebuild this bike for the less than the price of a new one, but I'm not sure why you're so eager to replace so much.
Here's what I would do -- based on what I have done in the past. I'm assuming you want to learn some (which you mentioned above) but don't own specialized tools.
Get enough tools to dismantle most of the bike (allen wrenches, some adjustable wrenches, screwdriver, etc.). Dismantle the bike -- you should be able to get everything off except the crankset, headset and front fork. Clean all the parts.
- Take it to a shop, and ask them to overhaul the hubs and true the wheels; overhaul the headset; and overhaul the bottom bracket.
- Figure out what gearing you want on the bike -- on that SR crankset you have, you should be able to get a smaller inner chainring to lower the gears a bit (perhaps a 24T or 26T).
- Have the bike shop give you the bike back with the wheels true, and an overhauled BB and headset
- Buy new tires, tubes, rim strips, chain, brake pads, handlebar tape, brake and derailleur cables, and cable housing
- If you don't like downtube shifters, get a bar end shifter conversion kit from Rivendell;
www.rivbike.com.
- Put the bike back together
I wouldn't do more than that right now.