Look up Sound on Sound's feature about the difference between Hi-Fi speakers and Monitors. Classic article.
Basically, until you get to a certain price point, cheaper Monitors aren't really any better than Hi-Fi speakers.
Nearfield Monitors as we think of them didn't even exist until the 80s.
A lot of pro audio people will tell you the important thing isn't what you use, it's familiarity with it. Loads of times it's better to work on something you have listened to loads of shit on, because you know how it reacts to music.
As far as headphones go, I'd say you need to make sure you have a proper discrete amp to drive them. Headphones into just an interface or a 1/8th inch computer jack is just shit. Some headphones sound fine being driven by things like Ipods, but a lot of the serious ones require an amp.