So many different films that each produce a unique image. It really depends on what you want.
If you have the money to buy a good film, Velvia 50 will blow your mind, especially for landscapes. Very saturated colors but has to be processed E-6, which is more expensive and harder to find.
For people I usually go for Kodak Portra if I have the money, the VC is slightly more saturated than the NC, comes in a 160, 400, and 800 ISO.
Black and white has a lot of options, I'm a fan of Kodak Tri-x or Ilford HP5+ or Ilfords Delta 3200 if I need some good high speed film
That said, I have still got great colors with expired Kodak Gold, I normally over exposure cheaper/expired films by 1/2 to a full stop, then adjust the levels in post processing. I find that this gives me slightly more vibrant colors.
The AE-1 is a very capable camera and should give you some great results. Make sure to post some photos once you get them developed!