Sure you can be a private. You need to have RIP (ranger indoctrine process) in your contract to have a definate chance at going.
Once you graduate basic and AIT you will be sent to RIP training (if its in your contract). This is a 2 week pre ranger course--if you fail out you will get sent to a regualr unit or can recycle into the next class. Its intense training to get you ready for Ranger School. If you pass RIP you will get sent to a Ranger Battalion as your duty station...this does not make you a ranger. You are only considered a Ranger once you prove yourself worthy of a spot to Ranger School and upon completetion, recieve your Ranger Tab. This school is completed in 3 phases.
Darby Phase- at ft. benning, ga. You will do land nav, swimming, helocpter jumps etc.
Mountain Phase- is Dahlonega, Ga. where you will repel walls and train in a mountain setting.
Urban/Swamp Phase- In Florida. and its exactly that. have fun with the gators. :)
It a tough but dignified school. Lots of soldiers never get the opportunity to go.
Special Forces traning is done at Bragg, NC. You have to submit a packet that you want to go and make is through the "Q course" or "Selection". You have to complete physical and mental training as well as master a foreign language.Training is done over the course of 2 years.
I do not think there is a rank requirement, although i can be mistaken. I would advise you to have Ranger School,some rank under your belt, and army knowledge before attemping SF.
good luck in your career :)
Myself- Husband work for Ranger School at Benning and is a SF hopeful.