After Army ROTC, what is the process of going to Airborne, Ranger, Special Forces, etc., schools?

Await a time with patience. Life is to lived and enjoyed. You cannot have two masters. When your mission has been completed, if you are still interested in ROTC, enroll.

Once you are actually in a ROTC program will be the time to examine your future choices.

If you really wanna know now, enlist, work and study towards an OCS program.

Focus on getting good grades in high school. Run cross-country and track even if you don't like the Run because the army makes you run 2 miles. The Army is also into push-ups and sit-ups though they're changing their physical fitness training starting in 2020. So working at the gym doing pull-ups, crunches, planking and using dumbbells or bench press is helpful. Many recruits go into basic training or ROTC with no physical fitness discipline. A balance of body and mind. Focus on your LDS mission for the time being. When that is done, enter a college that offers ROTC. You will get Soldier training there. Like the sergeant major said, you can always join a National Guard or Army reserve unit. Just make sure you do well in college. Don't worry about that right now. One step at a time. Don't worry about Airborne, air assault and Special Forces right now. Just focus on doing well in high school and enrolling in the proper college or university that has ROTC. You have over 1 million people in real life here on this social media platform.

Let me be the voice of practicality here. Whether you commission ROTC or OCS, Branch positions are both competitive and based on the needs of the Army. The way to give yourself a better shot at the Branch (as in Infantry or Armor, if you don't know the terminology) is to be as close to the top of the class as possible. I assume from your question that you are looking at Infantry, which is generally one of the competitive slots these days. If you get selected for Active Duty and you get your Branch Choice of Infantry, getting Airborne Qualified is normally pretty easy as long as you are requesting it from HRC, Ranger School will depend on what kind of unit that you going to on your first assignment since there are not enough slots for everyone and the priority are to units like the 10th, 25th and 82nd. OTOH, neither Airborne nor Ranger School guarantees you a slot in any of the Airborne units. Again, needs of the Army, but the higher you class rating, the more options you will have in unit choice.

Don't assume that the 75th and 82nd are the only tough units in the Army. The 101st and especially 10th Mountain were some of the toughest units I served with back in the day. I'm also told, but have no experience with the unit, that the 25th is a tough unit also. And don't discount the mechanized units, especially since that is where the real firepower in the Army is located.

Special Forces Officer is a different story. You can assess to SF from any Branch, but you have to be a 1st LT with at least 2 years of active service and be in your primary zone. Then it's a matter of surviving selection.

It's actually easier to enlist on a 18x option (Special Forces) or a 40 option (Ranger). If you qualify, it will at least guarantee you the chance to make selection.