I wouldn't go with AKG 701's unless you plan on spending thousands on equipment to get the best of them (seriously). I really wasn't a fan of them when I heard them, but they have a big following and do sound good with certain types of music.
Most people will tell you to get an amp or DAC, which really restricts your budget.
As wid said, Grado headphones are similar to the Axioms in sound. Grado SR225's or SR325's or Allesandro MS2's (brother to Grado) will sound fantastic out of just about any source like a laptop or portable music player. They are open headphones, so best for home listening. They are cheap enough used ($150-300) that you might be able to buy a small portable amp, too. Headfi is a great place to find used equipment that is generally well cared for.
If you'd like some closed headphones that isolate you from the world (and others from hearing your music) you'll have to decide if you want them to be portable or not. There are lots of options in each.
What music do you listen to? That might be the most important
