Hi, i am currently at OFT studying for my PPl. I`ll give you some tips for the TSA. get your visa first, then when you apply you can attach a scan of the m-1 visa to it, that way they know you have a student visa. Then just apply for the PPL clearance first. DONT apply for all the ratings at once. If you bother to read the small print like i did, you will see that each individual clearance enables you to 'commence flight training per rating withing 180days and must finish within 360 days'. Thus, if you apply for all 3 ratings at once, you would have to have started training on your last rating within 6 months of receiving clearance. Also, clearance is from the date you receive the clearance email, NOT the course start date.
I started my course 7th jan, but had my clearance for my PPL beginning of oct, so i had plenty of time. Once my ppl is done, i`ll re-apply for clearance to do my IR, and again for my MEL.
Also, if you have time, send your fingerprints off from the country you live in, that way you will receive your clearance before you arrive in the USA and you can start flying straight away.
Hope this helps, some words of wisdom from someone whos been thro the system with no problems. A