If I were to build a collection of components for my 'ideal' development kit, what would they be? What values of resistors, capacitors, leds, ICs, etc. would be most usable?
you will probably need a lot of of plug connectors for the connection headers on the board. don't forget to buy an acceptable amount of these 
you will also need some 220 ohm resistors (these are very often used, i guess because 5V, which is the mostly used voltage, divided by 220 ohms is something like 20mA, which is the highest amperage which a microcontroller pin can deal with). but also higher resistors will be usefull. 1k, 10k. but if it's not that important: if you run out of higher resistors, you can combine smaller ones. in most cases you won't need resistors with Mega Ohm values.
most LEDs have comparable values, so feel free to get what you like.
some transistors would be fine too. i bought some 2n2222 and some tip120 transistors. i don't think, that i will need more than these during the next weeks.