Comment by buescher
The TL081 family of op amps is definitely in the "old parts you should (sometimes) use" category (for price/performance) but there have been much better op amps for not much more money for a long time now. Both the now-ancient 2nd edition and the aging 3rd edition of Horowitz and Hill recommend the LF411 for a JFET-input general purpose jellybean, for example.
For learning you some analog, I would recommend the LM358 op amp and the LM393 comparator and all the old National material on them. The LM358 has its quirks so you won't think op amps are ideal but you still see them in a ton of stuff, because they're dirt cheap and adequate for a lot of things, and the LM393 comparator is still so good you really should know why you're choosing anything else - micropower or exotically high speeds or whatever.