Another “what can you afford” question. Most editing programs have the ability to do simple effects, including chroma keying (green/blue screen). However, programs dedicated to effects (or extra plug-ins you can buy for most editing programs) will do a much better job than whatever comes standard with your editing program.
After Effects is a popular choice and you can easily get help/advice from thousands of people on the web.
If you are serious about perusing a career in visual effects, Shake seems to be the big up and coming program these days. My personal choice for the most bang for the buck is Combustion, which also has a decent foothold in professional effects studios.
Honestly, if you’re just starting to get into this whole movie making thing, I suggest you concentrate on learning how to use the basic tools to tell an entertaining story before you get caught up in the eye candy. A visual effect should contribute to telling the story. If you don’t know how to tell a story first, you won’t know how to make the most effective effect.