You can buy a few kits to get most values as a starting point, then just refill when you start running low on certain values.
Keep in mind with the following things I'm posting, these are just ideas of things you can consider buying, I didn't go through these and verify each one as a good purchase of quality parts, I'm just recommending kits like this.
Box Caps and/or These Poly Film Caps (the box caps and the red/green type of caps are usually the same value ranges
Diodes (and maybe buy a few germanium diodes later on if you feel like fucking with that, but that kit should last a while and handle most diode needs)
Op Amp IC's - most of dual op-amps are interchangeable and it takes some cork sniffing to detect a difference, but get some 4558's, Lm358's or TL072's, etc. etc. - a different one would be an LM741 since it's an older part that's a single op amp and not dual op amp. You can modify circuits to accommodate the pin difference though. You might also want some quad op amps like TL074's (Jfet), or a hex inverting buffer like 4049's - with these, maybe wait til there's a circuit that requires one before buying any.
Other IC's - buy them as you need, but 2399's are used in a lot of modulation circuits.
Transistors - This kit should be a good starting point. Load up on common NPN silicon types, but hold off on germanium until you're more sure of a specific project you're making that will require them, especially PNP types. You're not often going to be using PNP Ge unless you're making very vintage fuzz face types of circuits. Beyond that kit, maybe get some J201 and/or 2N5457 JFETs. J201's are very common in circuits. I also find having 50k and 100k variable resistors helps with biasing these on the drain side. If you want JFET's to work correctly, you need to bias them and can't just throw them in a circuit with some static resistor value.
Pots - Hard to say, but common values like 10k, 50k, 100k, 250k, 500k, 1M in both A and B types. You will actually find C types in pedals sometimes, but wait til you need to load up on those for a specific project to buy any. Alpha.
Multimeter, don't expect to get very far without one.
This tool is awesome and cheap. I use it CONSTANTLY! Before I put any part into a circuit, I test it to make sure it's good with this. It's so cheap and underrated, I can't emphasize enough how much I fucking love this thing. It will also tell you the pinout of transistors and hFE. It has readings that are very close to my much more expensive Atlas DCA (which I also highly recommend for testing transistors).
Breadboard
(edit: accidentally listed 2n3904's as op amps, they're transistors, common ones that you might want to just stock up on a few.)