Organize organize organize -- nothing is worse than knowing you have the part, but can't find it in your stockpile.
I really want to stress this. The more parts you have, the more critical it becomes. Give some serious thought to your organizational system. It may undergo many revisions, with each successive migration taking more time:
1) I started out with those common part organizers, the ones with lots of pull-out drawers, that can be partitioned in half. They're ok for rapid access to a few parts, but each separate area tends to waste a lot of space. And they don't travel well! I took them in the car once, and they got tipped over. What a mess. Some drawers opened and parts flew out. Some drawers got jammed by parts so badly I had to destroy the drawers to remove them. Parts traveled surprisingly easily between drawers and partitions, getting mixed together.
2) Next system - Plano Stowaway #3600 series boxes. The specific variety that can be partitioned in up to 24 areas per box. Apparently not sold separately anymore, included only with a larger organizer that holds 4x boxes, which I also use; if interested, I can look up the model #. These served me well, and still do. They travel without issue. Though each partitioned area may still waste a lot of space. At some point I got a few hundred smaller hinged-top plastic boxes, cheap via surplus outlet, that fit well and further subdivided the space. But eventually I ran out, and though I searched extensively, I couldn't find the same item. All similar replacements didn't fit as well, and were much more expensive. Also, when my parts collection grew, moving around partitions, boxes, and parts to keep similar items together became quite a chore.
3) I'm gradually migrating to use of a lot of Ziploc-style bags, of many different sizes, some quite small. These waste virtually no space, if you press the air out before sealing. Sometimes I don't get all the air out, so I typically poke a little hole in the bags to let the air escape, pressed out by the weight of other bags. And I have a Brother label printer to make nice self-adhesive labels.
3a) For frequently-used parts, I still use the Plano 3600's. For example, I have a 3600 for most resistors. For 1/4W leaded, each partition holds a decade (0-9.9ohm, 10-99ohm, 100-999ohm, etc). The individual values are kept in bags within the appropriate partition. I have fewer 1/2W leaded, those get just a couple of partitions with bags. Another partition for current measurement shunts. A few partitions for trimmers. And so on.
3b) For lesser-used or bulky parts, I use a nested bag system. For example, I have a medium bag for diodes, containing smaller bags for switching, rectifier, fast recovery, varactor, and Schottky; and each of those containing tiny bags for each part # and value. The medium "diode" bag goes into a Rubbermaid bin for "semiconductors", along with transistors and such (not including IC's, I have enough of those they get their own bin). Power resistors and large potentiometers would take up too much room in the 3600's, so they all get bagged and binned.
It takes a while to collect many different parts for a project, but at least I always know exactly where those parts are. The alternative is chaos and a lot more wasted time.
I will also warn against buying random part assortments where the parts are not already sorted/separated and clearly labelled. No matter how incredibly cheap they may be. You will put off sorting them. When (if) you finally do, you will typically find lots of oddball parts and values, that you'll then feel obliged to spend time organizing when it will probably never benefit you.
I bought some SMD ceramic cap and resistor assortments from an Ebay seller. Each value is on tape, and the value hand-written on the tape. But not particularly legibly! I don't regret it, but I had to spend some time relabeling them all, including testing those for which I was unsure. If I had to do it again, I'd try to buy from a listing that includes a picture showing the seller's handwriting.
For orders from traditional large distributors, I prefer Newark over Digikey/Mouser. Not just because they're cheaper in general, but because they print part specs in a small square on the invoice, that can be cut out and taped onto something as a useful label. Big time saver. They used to include a separate sheet with the same info printed on actual peel-and-stick labels, but I haven't got that with my last few orders; either they stopped doing that, or they do it only for orders exceeding a certain size (my last few orders have been smaller).
Buy some panels of anti-static foam that you can cut down to size as needed. And some anti-static Ziploc-style bags of various sizes. You'll need them to repackage ICs and static sensitive discretes that you receive packaged in ways incompatible with your storage system. Schottky diodes are static sensitive, unless they have an integrated guard ring, so when possible I get the latter to reduce special packaging and handling requirements.
Some useful "jellybean" ICs that I think everyone should have, whether you want them in DIP or SMD (or both) is up to you:
* LM393 (dual) and LM339 (quad) comparators (same specs per each comparator)
* LM358 (dual) and LM324 (quad) op-amps (same specs per each op-amp)
* TL084 quad JFET op-amp
* TL431 shunt regulator
Supplement with special case op-amps as needed. I like to have a few rail-to-rail varieties on hand, MCP6002 is good for relatively slow signals, MCP6294 is faster; but they are by no means the only options or even clearly superior, they're just what I quickly picked to fill a possible need. And in fact I've never actually needed them.
For digital work, a variety of 74* series logic ICs may be handy. In particular, the 74HC family, which seems most useful for interfacing to any other logic family, and isn't too expensive. But there's still a lot of parts in that family, you'll have narrow it down to what you think you'll use. If you get into MCUs, and use those with sufficient number of pins that you don't need to multiplex input/output signals, you may never need any of the 74*.
The KIS-3R33S is a tiny 3.3V 3A switching regulator module, available dirt cheap on Ebay and such. Can be modified for other output voltages via external feedback resistor or modification. I bought a few dozen of them for something like $0.20 each, love them, and use frequently whenever a switcher shows clear benefit over a linear reg. Always put at least a 10uF ceramic or low-ESR electrolytic on the output to ensure stability; or if you want low switching noise, use a Pi filter (cap-inductor-cap).
I could go on and on. You will always find yourself in need of something. And in trying to prevent that, you will always buy a lot of stuff you will never end up using. Plus your needs will change as time goes on. Whenever you think of something you'd like to have, but don't need immediately, put it on a list. Whenever you need something immediately, evaluate your list, and also order the items on the list you want most; feeling free to leave low-priority stuff on the list. You may find some things stay on your list a long time, until you decide you really didn't want or need them after all.