As the others have said, the Nike Pegasus is usually a good dependable first running shoe (BUT DO TRY THEM ON FIRST). Some find it too firm, some find it to soft - I think this is a good thing for a first shoe - pick a dependable shoe that is in the middle of all measures. From your time with the Pegs you can then work out what you want for your next pair, softer or harder, etc. After a few iterations, and a few bad decisions, you'll arrive at your perfect shoes (for how you are then, not the perfect first shoe).
I started with a pair of Reebok Road Lite, attracted by the price tag and thought I was only running a single charity run. Once I got hooked, my next 4 pairs were Pegasus, before I moved to some bad decisions (The Asics Nimbus/Mizuno WaveRider/Brooks recommended by gait analysis were not for me) and finally finding my shoes/brands at Skechers and, more recently, back to Reebok. I may well go back to the Pegasus for long easier runs, and I do have fond memories of the old Pegs.