Are there any requirements to be selected for 8th and I?

have to go through SOI ITB, so your going to be a grunt by the end of your 8th and I assignment, or be transfered somewhere for presidential security, you need to pass a pretty high clearence, dont know if its secret or confidential but you need a clearnence....other than that im not sure.

Yes, there are clearances.
Often the Drill marines there are indeed Infantry. I didn't know any there that were not with the Drill Platoon's. They did there Infantry training usually during non-ceremonial season which was usually done in Quantico, Va. Sometimes, we would also train with or even teach some of the Officer's in OCS.
There is a Guard detachment which is Security Forces folks. Members from the Guard are the ones whom are picked to be closer to the President and that includes Camp David and the White House.