Yeah, you can get a bunch of general purpose diodes. For low current, the size is not important. If you need them for current clamping around motor drivers, get ones that can handle the back-emf currents. A selection of zener diodes might not be a bad idea either.
For transistors, I have a bunch of general purpose NPN and PNP. I like the 2n2222A (the A suffix is higher current) for a NPN. For larger current apps, check out the TIP12x series. You can get matching NPN/PNP sets, which is handy for building things like H-bridges.
For really high current apps, you can try our FETs and other fancy stuff. I haven’t bothered yet, but I don’t have any really big motors to turn.
Another very handy IC to have on hand is a voltage regulator (just thought of that). This way you can use batteries and supply a nice clean voltage to your electronics. Look for a Low Drop Out (LDO) model. That will let you operate even with a small differential between the battery supply and the output voltage.
Transistors were the first to come to my mind after resistors and Caps…diodes are extremely useful as well, I have used several small signal diodes on many occasions. Not sure how they were missed on the first response. :)
The most commonly used electronic components vary according to the project, but of course transistors and diods are the must have components you’re likely to use in any DIY electronic project. There are many online and offline places where you can buy wholesale electrical supplies or you can just go to your local hardware store. Still, ordering them online is cheaper, and overall a better option if you don’t mind the delivery time.