How do does it take you to start basic training after MEPS?

It's really just depends. I've known people who went to MEPS sign their contracted and shipped out to Basic Training within 30 days, but I've also known of people shipped more than 90 days after signing their contract.

Right now, the Army is offering bonuses to recruits who ships out, within 30-60 days after signing their contract if that's something you're interested in. Also a cool thing about this particular bonuses it can also be combined with other enlistment bonuses according to the Go Army website.

Depending on the job cause when my brother joined on a Friday they had people shipping out that Monday but his ship date was 1 month away!

It depends on the ship date of the job you pick. If you pick something with a long AIT that only runs 4-6 classes a year, the next open seat could be a year away. If you pick something like Infantry, it could be 2 weeks or less.