A lot of components are of a standard size. Dig through the standard Eagle libraries and find your components, then look at the specs and datasheets to verify they match. Eagle also is pretty good about showing you sizes on the screen, and I'm pretty sure you can print the layout to paper to see if your components fit. Not to sound rude, but I think you may be making it harder than it is.
Another thing that helps me when tracking down a component in Eagle is to download an Eagle library from one of the smaller distributors. Sparkfun and Adafruit both have libraries that pare down the choices, and most times the components you will use for all but the most obscure parts will be listed there. And remember, there are standard size packages for a reason. A 14 pin DIP is a 14 pin DIP, no matter what the IC is doing.
As far as placing the parts on a PCB, that is an art and not a science. (Well, there is *some* science...) I take inspiration from other boards--I lay things out after looking at other PCBs, just to see how they did it. And when it comes time for the traces, I straight out cheat. Auto-route. That gives me a starting point. It's nothing to go back and change things up a bit if needed. All that being said, everything I've done is pretty drop-dead simple, so this advice may not translate to more complicated layouts.
Good luck! It was/is sometimes very intimidating. I just think about it this way: I'm prototyping. Prototypes are never right the first time (unless you are insanely lucky or again, super simple). Learn more each time you do it and keep up the fight!