Hi Jim,
Thanks for the post; this is a damn good question!
To start out, you want an inexpensive meter you can happily destroy with inexperience without losing too much money.
Fortunately, since the advent of China as the world's factory, prices are not high. There is a huge choice.
This is what you will need for building AKSAs:
1. DC and AC volts to 200. Higher is nice, but not strictly needed.
2. DC milliamps to 200.
3. Diode test.
4. Resistance down to 1 ohm, up to a megohm. On a DMM, the ranges are typically 200R, 2K, 20K, 200K and 2M.
5. Transistor beta (hfe) test function.
You do NOT need capacitance, inductance, or frequency, or phase angle, or any of the fancy stuff. If you can't get a beta test function that's OK, it's just handy. You should not spend more than about $US30 on this meter, which is, of course, digital.
When you are thoroughly experienced (= two AKSA projects!!) you can graduate to the more expensive meters. My advice here is a lower cost Fluke, arguably the best meters of all and made in Seattle, WA. I have about four DMMs, but the best of them, and used ALL the time in my workshop, is an entry level Fluke Model 10, which is autoranging and cost about $US80. The best Flukes are complex beyond reason - they can measure the mood of your Mother in law at 10 miles - but they cost the very planet we live on.
Hope this is helpful,
Cheers,
Hugh