You are cutting it close to the age limit so get in touch with a recruiter ASAP to get the process started.
I got 4 or 5 letters of recommendation and my recruiter read them all and helped me choose the best 3. I would recommend this. Personally, I'd say one academic, one professional, and one community-oriented (like from a volunteer supervisor, mentor, or something like that) letter would be an ideal mix.
The chances of getting accepted honestly depend on how many people they are taking in the year you apply.
Read the OJAK (Officer Job Aid Kit) and get in touch with a recruiter.
Also, for future reference - you don't "join" OCS - you apply to OCS to eventually earn a commission.