Would a point and shoot with a zoom take good, clear pictures, of high enough quality to be accepted to Airliners.net?
It can be done (I have a few that are on the database that were taken with a P&S), but you need to use really good film and get good scans. A P&S is good to start out with if you are just getting into photography, and want to learn some concepts. However, if you are interested in getting really high-quality images, you will eventually want to explore the option of getting an SLR. I started out with a P&S, and it served its purpose, but I didn't start getting images that I was really happy with until I started using an SLR.
A P&S will serve you well if you are primarily interested in shots where your subject is stationary. But for any shots involving motion, such as takeoffs, landings, approaches, you will want to use an SLR because you have more control with the shutter speed. Finally, the optics on an SLR are just far superior.
As for film, if you use a P&S, you will want to opt for film with an ASA of 100. Anything above that with a P&S will result in unwanted grain.
I don't want to carry a big clunky camera around
You'd be surprised - there are several types of SLR cameras that are light and compact.
Whatever type of camera you decide to buy, have patience, and practice, practice, practice. You may not like your initial results, but once you have developed a feel for what works and what doesn't, you'll start getting the type of results you are looking for.