Try this for a starter:
http://www.diyfactory.com/projects/jlmsimpledi/jlmsimpledi.htm
This was my first project and its pretty straight forward. It's a damn nice DI (as is all JLM stuff). The kits about $40, then add about another $20 for parts from Jaycar (the main cost being a case) so your total outlay isn't too high for a first project (if you fry it, you're not too badly out of pocket). There's no instructions, but when you look at it it's pretty self-evident where everything goes, so long as you get the polarity right on the electro caps and don't do what I did and put the opamp in around the wrong way (what's that smell?). Plus Kev's page that I linked to above has some useful pics and info that will give you guidance. Finally, you're dealing with a 9v power supply rather than a mains power supply, so your ability to cause injury is kept nice and low :P
My second project was a Paia Tube Mic Pre kit. It's not a great sounding pre IMO, being a starved plate design and all, but it's damn easy to follow (the instructions are superb), you'll learn a truckload and its based on both solid state (opamp) and tube circuitry, so you learn a bit about both types of circuitry. It is cheap - around $250 for 2 channels, although I replaced a number of parts (better quality connectors, switches, bezel-mounted leds, a more solid case, etc) because Paia keeps costs down by using low-quality parts in some areas. I'd highly recommend it for learning how to DIY, but it will become a door stopper in most studios pretty quickly.
My third project was a G1176, and my fourth a GSSL. I was very glad I had the Paia under my belt before attempting these, as there's no manual to hold your hand as you go - just an amazing forum (Prodigy Pro, of course) that has the answers to nearly any issue you might have.
Another suggestion is JLM's Baby Animal pre's. The posts on these at Prodigy Pro suggest these sound fantastic, plus they look pretty straightforward to build and come in a kit (but without any instructions, I believe). JLM offer a power transformer for this kit which also simplifies things nicely. At around $150ish per channel (plus case, connectors, transformer, knobs etc) they are incredibly cheap for what you get, plus very flexible as they are designed to work with a wide range of input and output transformers, each of which has a different sound and different application.
A number of people appear to have built these as a first project. Relatively speaking they look pretty cheap. And even better, if you build the JLM DI first, then you can convert it into a DI for a Baby Animal so the two projects come together nicely (I have two DI kits built - one is a traditional DI box, the other is sitting in a drawer waiting until I have the $$ to buy some Baby Animal kits).
Does that help?
Chris L