Ok,
To answer some questions, from what I gather airlines don't care what kind of degree you have as long as you have a degree. You could have a degree in basket weaving it doesn't matter... I would choose something you enjoy like engineering, just in case you find yourself furloghed and in need of money.
To answer your question about jet time and turbo prop time. Jet time is not the same as turbo prop time. Jet time is when you are flying an aircraft that has actual jet engines or also known as turbo fan engines. The turbo props are jet engines but with props instead of the high bybass fans on larger jet aircraft. You usually start off flying a turbo prop like a Saab 340 or Beech 1900D. If you are lucky then might get a job flying an RJ but remember its the upgrade time to Capt thats important. The PIC jet or turbo prop time is very important. Most major airlines want at least 1000pic multi turbine time. If you go for the RJ look for a company that has a 2-3yr upgrade time. Thats reasonable. Others operators that have turbo props typically upgrade in 12-18months. So its all how quickly you want to get there.
To answer your question about choosing the flight school. Choose one you comfortable with that has a good reputation and good maintenace. You don't want have to set an airplane down in bushes because of careless maintenace errors.
Good Luck hope this helps
Chris