Don't pay the school up front. Paying a little in advance is fine, but don't trust a school that wants everything up front. They have a nasty habit of going out of business.
You have two basic methods: Part 61 schools, and Part 141 schools. "Part" refers to the section of the Code of Federal Regulations (sometimes referred to as the "FAR's") that provide the rules for the training you'll undergo.
Part 61 schools are generally less structured, more tailorable to your needs. Part 141 schools generally use a strict syllabus, with regular checks on your progress.
You'll be tempted to think that your flight instructor is highly experienced. Usually the flight instructor is the least-experienced pilot in the industry, and it's a "time building" entry-level job. Keep that in mind when shopping around for an instructor. Try to find one with more experience. Remember too that flight hours don't mean much; a 20,000 hour pilot with 10 hours of instruction given is a 10 hour instructor. A 300 hour pilot with 50 hours of instruction given has five times the experience, which is still just a drop in the bucket. It's best to find an instructor who has more flight experience and more instruction experience. You're learning judgement as you go, and those without experience often only know what they've been told...and it's not always correct.
High-wing vs. low-wing in a training airplane...doesn't make any difference.
Look for value, but don't scrimp. Many rental places and schools do minimal maintenance. Schools that also run charter services or that have maintenance repair stations attached often have better maintenance. While the outward appearance of the aircraft isn't really a good indication of the actual mechanical condition of the aircraft, it's a good place to start.
Don't get too caught up in schools advertising all the bells and whistles in the aircraft...GPS and display screens. They're not necessary, and you may be better off learning the basics without too many gimmicks on board.
When a school tells you that you can complete the private pilot certificate in 40 hours, they're telling you about the FAA requirements. Students typically take longer...about 70 hours on the average...which means the cost will be about 35%-50% more than what's advertised. You'll also have other expenses, such as a headset, which can add anywhere from a few hundred to a thousand dollars to the cost.
The more frequently you can fly, the better you'll progress. Shoot for two or three times a week, if you can. The more you space the lessons out, the more time you'll need to get through the training, and the more it will cost.
Ground school is a good idea, but not necessary. You can order training videos or CD's. Most are pretty good, except the King series. Sporty's or other pilot supply places have them. Aviation organizations (AOPA, EAA, etc) and aviation web boards are good places to start.