There really isn't a need to "request info" from residency programs. You can find most info on the internet, either through their own websites, Frieda, etc. It's also extremely helpful to do an externship at the programs you're most interested in to get a really good feel of the ups and downs of the program, including any dirty laundry that they dare not bring up on interview day. This will also allow the program to get to know you and consider you more seriously as an applicant.
As for timeline, you can start researching programs sometime in spring or summer, as early as April for you early bugs or as late as July or August for procrastinators. Many people chose which programs they'll apply to based on location, but if location holds little value for you, then you'll need to spend more time researching all the programs throughout the country. Deciding whether you want an academic vs community program will also help narrow down your search.
You should start working on your ERAS application over summer as well. The gung-ho people submit them as early as August, but the actual deadline is November 1st when the Dean's letter is officially released. You'll find that some programs (usually the more competitive ones) will not even look at your application until the Dean's letter is released, whereas others will start offering interviews beforehand.
Letters of rec should be requested at least 2-3 months prior to Nov 1st. Doing so will give the writer ample amount of time to write it, and for you to follow up on it in case the writer forgets to write/submit it or has to leave town unexpectedly.
Hope this helps.
