Digikey seem to be edging up their 1-off prices, but with a $250 budget, I'd look to spend that in maybe two bites.

Get the Toolsticks, as they are cheapest, and one base at ~ $20 then 2-3+ Daughter cards as they are only ~$10, so are close to disposable.

If you like DIP/PLCC, then also order some Atmel AT89LP51xx, they can boot-load cheaply.

For Multimeters, they all do V-I-R, so look for one that also has C & F.

eg Mouser 685-EX330 is 40MHz counter & Duty Cycle, 4000 counts, @ $59.99.

With 40MHz and Duty, you can use it as a logic-probe up to the toggle rate of any 8051.

For links to PC, I would get something like UM232xx - FT232H device, with Xtal Baud rates and choice of form factor. $15-20

There is also UMFT231XA, but at the same price, the FT232H is a better choice. (this can boot load the Atmel devices, and talk to any TTL RS232 system)

You can also make a low cost frequency generator using FT232H & use it to calibrate the FreqCtr on your Multimeter.