jacmom,
I've never used Priceline for booking airline flights; I've heard mixed reviews from various people so I'm reluctant to try it. (I have used it for hotels in the U.S., though, and it's been fine) If I book online, I usually book directly through the airline's website or Expedia.com
I recently read an article in the New York Times about several websites that search many, many different airlines for the best prices on flights. You can't book through these sites, but they show you days when it's better to fly, etc. You can read the article from February 21, 2010
here.
Since I read the article, I have been watching fares to Madrid on Kayak.com with the hopes I can make a trip over there this year. It shows you how long the trip would be with the layover, etc.
As for the European airlines, as MadridMan wrote, there really aren't any sketchy ones that you would have to worry about. In fact, coming from the US, you would most likely fly on a US-based airline. Since you're coming from the West, I'm not sure that you would be able to have a direct flight. So, you'd probably pass through one of the following: Dallas (American Airlines), Chicago (American Airlines), Atlanta (Delta Airlines), Philadelphia (US Airways), Washington Dulles (United Airlines), etc. Many of these airlines have partnerships with European airlines.
For example, with American Airlines you might fly on Iberia Airlines or British Airways for one leg of the trip; with Delta Airlines it could be Air France or Alitalia or KLM Royal Dutch Airlines; and with United Airlines it could be a flight on Aer Lingus or Lufthansa. In these cases your layover might be in London, Frankfurt, etc. Many of the European airlines are nicer than the US airlines; I've flown on all of the airlines I just named and they were all very pleasant.
Good luck!