So this is something I actually enjoy, being a graduate of one of the state military institutes.

I am going to limit my answer to the Regular Army, as the numerous spots which would need to be filled in State Volunteers or National Guard would mostly be handled by the individual Governors of the states.

Even before the founding of West Point it was and still remains the right and duty of the President to appoint and give Officers their Commissions. Though for lower ranks local commanders of the Secretary of War could essentially just forward names for the positions and have them approved. That made political connections very important. And while West Point did provide many officers in the small army, most anyone of good moral character, some education, and not a criminal might write the War Dept applying for a commission.

State run military schools were also a long standing source, with VMI and The Citadel as two prominent ones, along with Clemson, LSU, Virginia Tech, Texas A&M, and Norwhich amongst others. Officers on active duty would be appointed to the schools as instructors and periodically the student body would be inspected and interested graduates could seek a commission, it should be noted that all this predated the formation of a nationwide ROTC system by decades. It comes down to the original requirements of Land Grant colleges from the Land Grant act of 1862, which along with the sciences required instruction in military tactics, which some schools took more seriously then others.

(Side note, you can see a vestige of the requirement in the film Animal House, there is a scene where all the pledges take a few hours military drill to fulfill the requirement, despite not actually being in the ROTC program, then the Delta's use their drill area as a driving range)

ROTC got its real start just before US entry into WW1. Starting in 1915 in Plattsburgh NY, at the insistence of General Leonard Wood, a summer training program was created. Essentially it was like Scout Camp, but with the goal of taking college men and training them int he requisite skills of an officer to command troops. The students had to pay their own way so that greatly limited who and what type of men could attend, but the 40k or so students trained by 1917 provided a great many officers for the AEF.

The Defense Act of 1916 was what created an on campus ROTC program but it did not graduate anyone until the 20's. With the initial options for the Army being Infantry, Engineers, or Coast Artillery, eventually the opportunities diversified, and all the services came aboard.

There never really was a large or organized selling fo commissions for a few reasons. One was lack of interest, who Wanted to sit at some fort int he Mid West or Great Plains watching natives all day for little money and few chances for promotion? The other was that all promotions and transfers were at least examined by the War Dept and central control was much easier int he tiny Regular Army then their European peers.

Hope this helps! Feel fee to ask for clarification on anything!