Ken, if you got 20 years of use out of a Radio Shack DMM, consider the original purchase price money well spent. The only multimeter that I've ever gotten longer useful life out of was my trusty old Triplett 630 analog, which is now close to its 50th year in service.
For an inexpensive DMM, the Wavetexk 5XL is both rugged, accurate, and hard to beat for it's price. Mine is now going on 10 years old.
For extreme precision and accuracy, although it's probably not needed for most routine electronics and computer applications, buy a Fluke. I use a Fluke Differential Voltmeter for my primary calibration reference. I don't even own a Fluke DMM, because they provide far too much pecision for my day to day needs, and I would be heartbroken if I happened to drop one of these $200+ boxes that I owned onto the floor. They don't bounce well, well the Wavetek generally does, although if it doesn't, a new one can be had for under $50. Something to think about.
I would strongly suggest that you keep at least one quality multimeter on hand as a "sanity check" on your DMM, since DMMs often come up with some off the wall readings (even the Flukes) when their batteries begin to go south.
Just for what it's worth, the inexpensive Wavetek provides reading good to three decimatl place, but in all honesty that 3rd place is usually
+/- 2 when compared with an accurate calibration standard. With the exception of critical instrumentation measurments, not much work in electronics requires accuracy greater than this.
Hope this helps.
Harry C.
p.s., Some of the Radio Shack equipment produced 20 years ago was almost decent, but the stuff that they sell today is total throw-away junk.