My advice is to look for a mixed bag of resistors and capacitors.
An E12 set of carbon resistors between 10R and 1M should be good for most applications. You'll probably want to get extra common values, i.e 150R, 220R (for powering LEDs off 5V), 10k (general purpose pull-up) and 1M (for biasing crystal oscillators).
An E3 set of capacitors between 10pF and 10µF plus all powers of 10 up to 10,000µF are good enough for most things. Again you'll need extra common values, 22pF for crystal oscillators, 1nF and 100nF for decoupling IC pins, and 10µF for audio.
When I talk of E3 or E12 values I'm talking about the standard set of preferred values for components:
E3
10, 22, 47
E6
10, 15, 22, 33, 47, 68
E12
10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82
E24
10, 11, 12, 13, 15, 16, 18, 20, 22, 24, 27, 30, 33, 36, 39, 43, 47, 51, 56, 62, 68, 75, 82, 91
For example an E3 resistor set with values between 1k and 100k will consist of: 1k, 2k2, 4k7, 10k, 22k, 47k 100k.
When I mean powers of ten I mean 10, 100, 100 etc.