Unless you're designing the same function over & over, why would you know any part by heart? There's too many of them these days. It is easy to look stuff up online. I put everything I do on a schematic (expresspcb.com has a very quick to learn & easy to use schematic capture tool, easy to create a new symbol or modify an existing one) and check the wiring against that as I build it up, either on a breadboard (for testing or wirewrapping (using sockets soldered on perfboard generally, for more permanent creations. Occasionally I'll do an actual PCB if I plan to make more than one).
How else can you record it, share it with others, ask for help?
In just a couple of minutes, you can insert a couple of symbols, connect some pins, save it & post it to web via flickr or similar, and the world can give you some suggestions. How often do you see "my circuit doesn't work" followed by "post a drawing if what you have" from one of us?
And none of that fritzing nonsense - symbols with pin names so we can easily see that you have a NPN transistor being used to try and incorrectly switch the voltage source on/off vs the ground side for example.
Once you start using the proper tools, the design/debug gets a lot easier. Then the parts don't matter so much - you can make the same circuit lots of ways.
For example, suppose you need a shift out register, but don't have one, and further that you want to drive 4 LEDs in a string from 12V?
You can fake a shift register multiple ways - use an octal latch or octal register chip, like a 74xx373 or 74xx374, or some if its variants - xx573, xxxx574 (go to www.ti.com
and do a search for octal latch). Just wire output 0 back to input 1, 1 to 2, etc,
Then driving the LEDs you can use separate NPN, or N-Channel transistors. Or you can use a couple of 7406 (which is only a hex part unfortunately) which can take 30V outputs. Or a ULN2803, an octal version that can sink an impressive 500mA!
Best bet altogether is the TPIC6B595, which combine the shift-out register and the high current driverhttp://focus.ti.com/lit/ds/symlink/tpic6b595.pdf
So how you get to a final solution kinda depends on what you have on hand, and what you are able to get your hands on via online ordering, or sampling (TI just sent me 5 samples of tpic6b595 that I will try out in place of 74F374s/7406s I have wired up now), or scrounging out of dead electronics. For example, I have an epson inkjet printer with some nice motors, we are disassembling it while we come up with an idea of what to with it (ditched our forever drying up inkjet printers & got an HP CP1215 color laserjet instead - printing is now sweet!) - wife is thinking persistence of vision thing, I am thinking stepper motor? not so sure! But there also power supply usable parts - actually a whole power supply board that can be removed as one little module - nice! Will have to power it up & put meter on the output, see what is available )
Not much help I know when just starting out. Come up with a project idea, put it on paper, at least as a block diagram, submit it with questions "what would be a good part choice for this use in this application". Then when you start obtaining parts for a project, get a few extra, start building up a collection that you'll have for future projects.