Hey NoCO2,
I saw that you had roughly 3k miles on this bike, but didn't see if it was purchased new by you, or if you got it used. I am amazed that the cassette is showing wear after that low mileage, as I have ridden 3x - 4x that many and my cassette is still not worn out. It is a bit scratched form shifting, but could last another 10k with no problems. Take a look at the gear teeth on the gears you use less, and compare them to the ones you use more. I think you'll find the wear patterns are quite similar (meaning it's not as worn as they seem). As for the skipping issue, be very careful about 'cross-chaining', and that will make a new chain skip even on a new drivetrain, so again, your parts may not be as worn as they seem. Much like Lazarus, I only lubed my chain when I could hear it 'singing' as I rode, and I expect that is what you are experiencing. I'm even so low tech that I squirted it with WD-40, wiped it off with a rag, and rode quietly for another 2-3 months. There are a number of tools you can use to check for chain wear, and I highly recommend you getting one if you're concerned about this.
I would also recommend that you find a new bike shop, as I think you're getting some HORRIBLE advice from that mechanic. As for resources, you got a link to Sheldon Brown's(RIP) site, and that is an incredible resource (it's where I learned to build wheels), and the Park Tools site, but I would also advise you to get a copy of one of these two books...
http://www.zinncycles.com/books.aspx?book=roadbike
http://www.zinncycles.com/books.aspx?book=mountainbike
Amazon has them for $17 each, which is a great price for either.
Anyway, good luck with your bike, and I do hope you get everything working perfectly again.
Vol