As in most language learning, one starts with a small number (20?) of words and expands from there. APL also requires the neophyte to develop a mind mapping from abstract symbol to function. This may double initial learning time but I don't think that it's much worse than that. Mnemonics exist for many of the symbols.
But more fundamental is learning to map the problem space into an array formulation. This, not symbol application, is where a white board may come in handy.
Dyalog provides a free web-based tutorial that is quite comprehensive. [1] I daresay that spending a couple of hours with this tool will give you a great taste for APL. Spend a couple of days and you'll be quite proficient in both array-think and APL semantics.
Other useful tools include the wiki [2], a cloud server [3], and a neat examples wiki [4]. BTW, the "library of useful components" that the OP desires exists both as a compilation of useful idioms (code fragments) [5].
[1] https://tutorial.dyalog.com/ [2] https://aplwiki.com/ [3] http://www.aplcloud.com/ [4] http://www.jsoftware.com/papers/50/ [5] https://aplwiki.com/FinnAplIdiomLibrary