As a non-scholarship cadet you would complete the first two years without a contract.
A lot will depend on the number of contracts the Battalion is allotted for your year group. At the end of your sophomore year the Battalion will know how many contracts they have available, if any, most Battalions will have at least a few. The Battalion will select those cadets seeking a contract based on the Battalion OML for your year group. The OML will be based on your GPA, APFT scores, and ROTC Participation. If your sre selected for a contract you would start your Junior year as a Contracted Cadet providing you again pass your APFT.
Once you are contracted you would start receiving the ROTC Stipend and as long as you fulfill the requirements of the contract from that point on, you will commission upon graduation. Branching and Active Duty/Reserves selection will be the same process as all other cadets whether they are scholarship or not.
There is always the possibility that anytime during your first two years you could be offered a Battalion Scholarship, if they have any available. Selection for these scholarships are based on the same OML. If you are offered a scholarship then you would become contracted at that time.