I agree, those labs aren't much good.
Nowadays you can lean lots off the Internet.
As far as resistors and capacitors are concerned, start with a kit of E12 resistors (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 values) between 10R and 1M and an E3 kit of capacitors (10, 22 and 47 values) from 10pF to 1000µF. Most component suppliers stock such kits, failing that try ebay.
I'd recommend some comparators (LM311, LM393, LM399) and CMOS logic gates (CD4011, CD4001, 74HC00, 74HC04 and 74HC14) but don't worry too much about them as the most complicated problems are easier solved using MCUs.
Some voltage regulators are handy (LM7805 and LM317).
I also recommend a mains powered DC supply otherwise you'll find yourself wasting money on batteries or waiting ages for them to recharge. I would recommend buying a wall plug DC adaptor, rather than spending loads of money on an expensive power supply. If you buy a 15V wall plug, you can create a 5V supply and a 1.2V to 12V variable PSU using the LM7805 and LM317 respectively. For a bipolar +/-12V supply for op-amp circuit you could, use a 12VAC mains adaptor, an LM78L12 and LM79L12.
I can post some circuits for mains PSUs if you like.