Your chances of getting active duty are 100%. Once on active duty, your chances of getting into OCS are probably 60/40 or a bit better. If you go through active duty OCS, you WILL be an officer on active duty. Your chances of getting finance are slim which is MUCH better than most officers since it is the smallest branch.
MI is VERY selective and is one of the 4 most selective branches. You would have a 1 in 1,000 chance or less of getting MI. MP is much less selective. If you request it, you will probably get it. Infantry is usually at the top of the 2nd tier for competitiveness. You will get a LOT of academy graduates going Infantry. It is also the largest branch. Usually, Infantry will only take officers who put it as their #1 or #2 choice. Coming from OCS, it would depend on your course standing. If you aren't in the top 25% of your OCS class, don't expect to get Infantry.
If you plan to work for 2 years before going into the military, you will be in danger of ageing out of being OCS eligible. Most of the time, you need to be in a few years before you can realistically apply to OCS with recommendations from your commander and others. That will give you the "leadership" experience, but starting your military career as a 26 year old and planning to become an officer, doesn't make a lot of sense.
With a Masters Degree, you would be better off checking into the Reserves and going for a direct commission. That means you start out immediately as an officer. You would have a reasonable shot going that route and looking at AG (Adjutant General), Finance, and Civil Affairs. Civil Affairs was working a program for a while to accept people with Masters Degrees directly.