For Chrisebril:
Ask for your LORs NOW! The biggest hold-up during the app season is LORs, so you really want to get those done asap. Give the letter-writers a deadline, ask if they can make it, and follow-up with them to make sure they remember.
In terms of letters, two science, and then a non-science are good basic guidelines for professors. Then it is good to get some letters (1 to maybe 3) from ECs. You mentioned research? Definitely get an LOR from the person who heads your research. If it is just a grad student, have them write a letter and get the PI to sign it too (gives it more legitmacy). Letters from doctors you shadowed are ok but usually aren't given as much weight, so you may not need those at all. Choose your LORs carefully. Make sure they can write good ones. Also make sure you don't get too many. More than 5 is really pushing it, but doable, if you get good letters from a variety of sources (aka you don't need 4 science professors).
And if I didn't emphasize it before, ASK FOR THEM ASAP!
In terms of PS, it depends on you. Some write them fast, some slow. You can write a good PS in a short amount of time. Just get as many readers as you can. You want to make sure it makes sense and it conveys the message you want to get across. Getting a bunch of readers will make sure something isn't too vague, confusing, or can be interpreted poorly. It also needs to have just about perfect grammar.