Don't fall into the trap of buying packs of assorted resistors or (especially) transistors from china IMHO, you always end up with most of it sitting in the drawer and probably being thrown out when you die, or items that are so similar you sit there for ages figuring out which would be "best" to use, when frankly any random one would have done the job. Keep it simple, give yourself fewer choices not more.
For example, I don't keep a full selection of resistors, I don't need them, but the values I do keep are sufficient to do the job...
Through hole 1R, 10R, 100R, 1k, 10k, 100k and a couple of other "typically good for led [and zener] limiting" values 240R, 330R, and some 0R for diy pcb purposes. I don't use through hole much, so this rather course selection is fine.
Surface mount, 6 decades of each these 1, 1.5, 2.2, 2.7, 3.3, 3.9, 4.7 and 5.1 (ie, 1R, 1.5R, 2.2R .... 10R, 15R, 22R .... 100R, 150R, 220R .... up to 100k, 150k, 220k...), also 1M, 0R and some useful led-limiting-values 20R, 180R, 240R, 300R, 360R, 430R. I store these in pill organisers and use 1206 size. If I need other values I use the
resistor paralleler to get the ones I need
Add a few trimpots also, multi turn (3296 style) and single turn. The values aren't that important, 100R, 500R, 1k, 10k, 100k. Something like that. I use smd single turn.
Capacitors: 100nF, 22pF, 10uF, 100uF, 1000uF, and that's about it for general digital purposes where you are looking to decouple, or filter power supply rails mainly - but I don't do analog stuff, if you did, a bigger selection is warranted.
BJT: 2222, 2907, 3904, 3906 (all in SMD variants) and that's it. Add some ULN2003 darlington drivers, they come in handy occasionally.
MOSFET: One N channel and one P channel which have logic-level-suitable gate drive requirements and a reasonable current capacity (low RDSon). Personally I use Si2302SD, AP2305, and for less demanding situations the good old 2N7002
Diodes: 1n4007 (or 4004, whichever is cheaper at the time), 1N5819. That's about it, anything more "exotic" buy as needed.
Zener Diodes: 5v1, 3v3 for obvious slap-dash regulation reasons. 5v6, 3v6, 6v8, 15v for protecting against over voltage on various things (IC pins, mosfet gates).
LEDs: 5mm assortment, 3mm assortment, smd assortment (I use 1206 size).
Regulators: 5v, 3v3, 12v, and adjustable, in both through hole (LM78xx, LM317) and smd (various, I use 1117 series). Also, a few cheap DC-DC converter modules from China in your drawer can save the day.
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As for IC's, apart from the ULN2003 already mentioned, 74HC595 and 74HC166 shift registers, 74HC4051 analog switch, *324 op-amp or other fairly generic quad op-amp, optoisolator (EL817/PC817/LTV817 are common for through hole, EL357 for SMD), maybe some 4049/4050 hex buffers (useful for level shifting). And of course most important of all in the modern world, microcontrollers - whatever one floats your boat. I wouldn't bother with many other IC's than those for general on-hand supply.
Various hardware also I like handy:
5.5/2.1mm DC barrel plugs and sockets (panel and pcb mount, get round panel mount ones, easier to fit!).
Rocker switches for panels (power mainly), double throw best to maximise your options.
Toggle switches for PCB and panel, dpdt ones to maximise your options.
Standard 6mm tact switches, through hole and/or smd depending on preference. Some 12mm ones too can be nice.
A few panel mount pots and encoders if you come across them cheap, or just buy as you need. Again, with the pots, KISS, one value, maybe 2. Don't forget to have some cheap plastic knobs to fit them.
Insulated crimp terminals, bullets or spades as long as they are fully insulated. Ring terminals too (eg for ground connections).
Wire, get a good length of rainbow ribbon cable (comes in various widths from china in 10 way repeating colour sequence), a couple spools of general hookup wire in the AWG26-30 range, and some thicker stuff around say AWG20. Some twin core (figure-8) red+black would be nice too.
Misc small self tapping / wood screws, nuts, bolts in small metric sizes.
And of course loose alligator clips, test hooks, and banana plugs make it easy to make an extra test lead when you need it.
A generic relay rated for your mains voltage also handy.