Chiming in a bit late, but here are my 2c's...
Regarding the original question, my suggestion is to take a good dictionary (I like the Gallaudet dictionary w/ the DVD available at many libraries... or the NTID dictionary iPhone app) and just watch every video as fast as you can comprehend them and perform the sign yourself, either in random order or ideally in word frequency order (if you know how to easily). Watch as many per day as time allows, and push yourself even when you think you're getting tired. Do worry about reproducing the sign correctly (handshapes, position, motion, etc) but don't worry about memorization... visual/muscle memory is better than rote memorization, and you won't have perfect recall a week from now regardless. You will, however, have a much better vocabulary and general recognition of many signs. When I first started learning, I aimed for ~500 signs per day (about an hour or so/day), so the Gallaudet dictionary took me about a week to get through. I would repeat this every few months, until I recognized most of the signs, and then I started making shorter lists of signs that I had more difficulty with.
Regarding sentence structure, etc....
I agree that LifePrint is an excellent introduction. Yes, some of his signs are regional, but if you read his dictionary pages, he discusses regional variations quite well and more importantly, discusses how you should think about variations (e.g., ask local Deaf and use whatever they sign when signing with them). My recommendation is to watch the online lessons and then read all of the dictionary entries (there are only ~1000 of them, so again, doable in a couple weeks with some dedicated effort).
For more advanced discussions of sentence structure and Deaf culture, Google search "ASL green books" and look through the student and teacher guides. Pretty dense, but gets into all of the detail. I also found "Intermediate Conversational Sign Language" by Madsen a good source for glossed sentences, so you can see examples of how to communicate different ideas using ASL sentence structure. (My local library had all of these)
And finally, the absolute most important thing, as for learning any language, is to practice with native signers. Don't voice and practice having whatever conversation you can, even if it takes a long time. The best (and most fun!) way to learn a sign is by using it in conversation. There are a lot of psychological barriers to language learning... try not to think in terms of "getting in over you head" and don't be afraid to make mistakes.
Good luck!
