Jimmy,
I'm a former mech engineer turned pilot... Like you, after graduating college (2001) and starting work as an engineer, I started flying for fun and decided I liked it so much I wanted to be paid to do it. After training for about 3 years, I quit my engineering job in 2007 to go fly full time.
The fact that you are thinking about debt is good... I highly recommend you stay out of debt throughout your training process, regardless of how tempted you may be to get a loan at some point. I paid cash for my flight training as I progressed along, and I'm so glad I did that now.
As far as where to train, I would strongly recommend your flying club as long as you feel satisfied that you are receiving quality instruction. The 172SP is a nice plane, but a little pricey. If you can, try to do your training in a R model or even an old N model or something if they it. The old planes look raggedy, but they all fly the same. I didn't even use a GPS until I started flight instructing, and I'm glad it worked out that way.
Places like ATP are popular, but they are extremely expensive and the way they are setup makes them impractical for paying as your progress. Also, the aviation industry is in the tank right now, and probably will be for a couple of years. If you take a couple of years to progress through your training, your timing will probably be perfect. If you were just getting out of a place like ATP right now, or even a year from now, you'd be screwed as you just wouldn't have the experience to compete for the very few jobs that are out there right now.
Regarding regional airlines, you may want to consider expanding your goals. Although the airlines used to be a desirable career path, they've really gone downhill in terms of pay and quality of life. They treat their employees very poorly, and many airline pilots are bitter and hate aviation. I come from an airline family, and my uncle was a senior capt at AA and still hated his job. That really opened my eyes...
Fortunately, there is a large variety of civilian flying outside the airlines, including freight, charter, corporate, etc. As a former engineer, I determined long ago that I would likely be happier working for a corporate flight department due to my background. I already worked in business, so I was used to dealing with a corporate environment. I love the challenges involved in corporate flying, as it is not as structured as the airlines and requires you to think on your feet more often and you wear many different hats. Also, the pay and quality of life in corporate is usually much, much better than the airlines.
As far as the progression to get to corporate, there are many possibilities. After getting my commercial certificates (for single and multi engine airplanes), I started flight instructing. That is typically the first paying pilot job civilian pilots get. Some people do things like flying sky divers, flying traffic reporters around, etc. But those jobs are not nearly as common, and seem to be getting more and more difficult to find.
After flight instructing for awhile, I got a job flying charter in king airs. That was a great experience, and it really added a lot of multi time to my resume. Also, as a charter pilot you are flying to the same locations as corporate pilots and have very similar job descriptions. This leads to some very good connections in the corporate world.
After flying charter for awhile, I upgraded to captain at my charter company and flew passengers single pilot in a piper chieftain. That was a great experience, and really boosted my confidence and flying skills.
I finally got my first break into the corporate world last fall, and am flying a new citation with a great company in south FL. They pay is far greater than the regionals, and I also get a lot of time off. When we do travel, we stay in nice hotels and eat very well. I love it!
Anyway, that's just one example of the many career paths to a professional flying job. Keep your mind open, take your time, stay out of debt, and you'll probably have a geat time. Good luck!