Many "mom and pop" flight schools now offer part 141 curriculums as well. Training under part 141 rules means you are following a curriculum that's accepted and monitored by the FAA. As a result of this oversight, you can get your ratings faster. I think the biggest difference you'll notice is getting your commercial rating. 250 hours are required under part 61. There is no total time requirement and only a couple cross-country requirements under part 141. I had less than 200 hours when I got my commercial rating. This saved me a ton of money.
I agree with the others. There is no "best way" however, there is a way that's best for you. Second, don't worry about getting a degree from an aviation school. In fact, do something outside aviation and make that your plan B. You pilot certificate doesn't say how you got it. It just says you have it. Likewise, most aviation jobs that require a degree say nothing about it being an aviation degree. While some schools may have special reduced minimums if you went there, or had an intership with that airline, it doesn't do much for you if they aren't hiring in the first place and the only thing having more time does is open more options for you.