The Golden Rule of Med school applications: Be prepared, and be prepared as early as possible.
Get your LORs months ahead of time. Odds are, if there's a science professor you feel is worth asking, and will spend time writing a good letter, he/she is receiving the same request from many students. One of my professors said he spends a MINIMUM of four hours on a LOR, and got about 20 requests that semester. Of course, he wrote them in the order they were requested to be fair, which meant that the last few students had to wait quite a while for him to find the time for their letters.
Most major universities that have a med school and/or a pre-medical advising office will create a file to hold your letters. Therefore, you can get a letter LONG before you must submit it and just keep it in your back pocket until you do.
One last pointer about LORs: after someone has agreed to write one on your behalf, IMMEDIATELY write a thank you note/letter specifically thanking them for writing a medical school LOR for you. This has the effect of 1) reminding them to do it and 2) making them feel committed to actually getting it done on a timely basis.
As far as transcripts go, definitely use the AMCAS form. I tried to submit one ASAP without the printed form and it "got lost" until the third time I called AMCAS, used all the anger and fury that my bass voice can muster, and told the representative that my father, a lawyer, would be contacting them. A few hours later it was "found", with the excuse that the "unusual" (ie not AMCAS) form delayed its processing. Oh, and my threat was VERY viable because I had the foresight to use electronic tracking of the transcript. You can usually do this by bringing the FedEx/UPS/etc envelope ready-to-go to your registrar's office and requesting that they use it to send the transcript. If AMCAS tells you they haven't received it (which happens more than it should), you can simply say, "Oh really? So-and-so signed for it two weeks ago."
Let's see...more pointers...
Start saving money now for the AMCAS and secondary fees. If you're like the typical student, you'll probably have to borrow money from family, so you may want to bring that up now. Also, if you get multiple interviews, the costs really add up in a hurry.
Finally, triple check and edit everything you submit and make sure it's your best work. Stress over it while it's in your hands, but once any material has been submitted, just relax. You've got about a year before medical school starts (which it will, because you're good enough, you're smart enough, and darn it, people like you), so enjoy your last year of relative freedom.