As stated above, having a degree is better than not having one. However you don't need a degree and they are very expensive. You will spend half the money and get an airline job quicker without one. Time and money are usually the biggest factors. Your goal should be to get into the RHS as quick as possible. The first job isn't going to be a Major, it'll be a commuter airline: you'll need to turn up with an ATP and a pulse. You can always get a Degree part-time later on if you want to go for the Majors and still think you need one.
Some reading for you:
Part 61: Pilot certification.
Part 141: Pilot schools.
You can get your certificates under either Part 61 or 141, kind of like modular vs integrated. Kind of.
Airline jobs are flown under the rules of Part 135: Commuter and Part 121: Scheduled.