Should I wait and see if I can get a Ranger School slot or go to RASP and try to go to school while in battalion?

Ranger school is an advanced total soldiering leadership school. It will do nothing for your MOS skills. If you go RASP you will open up your MOS to the W1 course which is Paramedic equivalent and thus enhances your combat medic skill and ultimately translates to a solid transition to civilian paramedic and career ladder climbs. Go for the Tan Beret.

Do whichever one you can accomplish first. If you pull a dozen NCOs from regiment and ask which one you should do first, half will say one way, half will say the other. It comes down to which route works best for you in your circumstances.
There are a few things to consider for planning. If your unit sends you to Ranger school, you will be stabilized for a year afterwards. You will be promoted automatically to Sergeant without BLC once you are eligible. once you are eligible. Once you go to rasp oh, you still have to attend socm. That's 6 months long and during that time you won't be able to attend any ncoes. You'll need to complete that and most likely spend some time at the unit before they will send you to Ranger school.

You can always do Ranger School after RASP