Flight Training
I didn't set out to be a professional pilot when I started flying. I understand how you feel about only flying once a week. I would recommend, based on my personal experience, that you should just decide to do it, and start training full time. There are many ways to go about it.
I'd agree with UALX727 that a lot depends on your age. If you are under 25, you have a great many options open, such as the military. The military is a great option if you are young. The pros include the best, standardized flight training and flight experience anywhere, great personal development training as a military officer, the opportunity to do something for your country, and apparent hiring preference with the majors. The downsides include, well, the military isn't for everyone. A nine-year commitment, which won't matter that much if you're young. No guarantee of being selected or making it through flight training. The nine-year disadvantage might evaporate somewhat because there won't be much major airline hiring for the next few years. Military flying options include all the branches and your local National Guard unit.
If you're older than thirty, you don't have as many options. You can go to an aviation college full time or a commercial flight school full time. Or work and fly regularly at your local FBO. An advantage to an accelerated school is you build momentum and your training moves along. A few disadvantages to accelerated schools include too much learning coming at you too fast, receiving only enough training to pass checkrides, and your learning perishing after you complete the course because you are unable to continue flying. If you have a reasonable expectation of getting a job and/or continuing to fly after obtaining your certificates, an accelerated course may be fine. If not, with hiring the way it is, you may be better off in the long run in terms of thorough, retainable training to take it slower.
Most of the well-known schools are expert in helping students obtain financial aid. They do it to help you and to help themselves enroll paying students. You can obtain Pells grants and Stafford loans to finance your training. Payback terms are very liberal, something like seven to ten years. I took out loans to go to school for my current profession.
Finally, get your four-year degree, at some properly accredited college, in something. The majors hire pilots with or without aviation majors. You won't amount to much in aviation without a four-year college degree.
Hope this helps a little. Good luck with your plans.