You can do sleep fellowship after IM residency (or after anesthesia, psychiatry, neurology, or pulm/ccm). However, if you're not cross-trained in other areas, it may be hard to find work as a pure sleep physician (who can't see pulm, or psych, or neurology, etc)
For fellowship applicants - it's almost the same as applying for residency - MSPE from medical school, USMLE 1/2/3 (or COMLEX 1/2/3), LORs from your PD (a must) plus other faculty members, personal statement, lists of publications/awards/presentations. When I was interviewing applicants, I would try to find something from their application that was interesting to discuss during the interview (ie their research, their med school, their residency program, etc)
As a DO, you definitely want to go to a University IM program. Going to a community IM program will hurt if you're going for a competitive IM fellowship (currently it's GI, Cards, Pulm/CCM, Heme/Onc).
During fellowship, we rarely interviewed people from community IM programs ... the residents from community IM programs that we interviewed had impressive CVs (published in Chest or the blue journal, oral presentations at Chest/ATS/SCCM, impressive glowing LORs from their PD as well as their PCCM faculty, high Step 1/2/3, etc). I think within the past 5 years, only 1 fellow came from a community IM program ... the rests were all from University IM programs.
Don't discount Pulm/CCM just yet as a DO. While you may have trouble with the top tier programs (ie Pitt, UCSF, Colorado, Penn, etc), there are plenty of programs out there that are receptive to DOs.
So overall, aim for a University IM program, one that has fellowships in the fields you are interested, so you can gain research experience, exposure, as well as LORs (and on occasion, the friendly phone call to fellowship PDs on your behalf)