In my opinion if you want to enter the realm of portable set-ups the best DAP to start you off would be something like the Sansa Cip+ or Sansa Fuze. They are both fantastic players and I mean that. They are cheap, have a great neutral sound, both have native FLAC support, expansion slots, slot and normal FM radio not to mention you can rockbox them. For me I chose the Clip+ over the Fuze because I didn't need a big screen and valued the small size over a bigger screen and larger battery life. There are other great players out there but on a limited budget looking for a new player and 'phones you are better getting better 'phones like I said before. Hence why I keep saying the Clip+/Fuze is the way to go.
Other members may think differently but this is my opinion.
Ok moving on, if you want headphones that don't leak much sound you definitely have to look at the Sennheiser HD 25 -1 II. I recommend you look into it but when I did research into what portable headphones to buy they came up as the best for me. You should certainly read this thread http://www.head-fi.org/forum/thread/433318/shootout-36-portable-headphones-compared-beyerdynamic-dt235-added-05-29 by |joker| who compares 36 portable headphones. It's a brilliant place to start, but remember there are more headphones out there then what he has reviewed.
You may consider me bias as I own both the Clip+ and HD 25's but I did my research before buying either, so I know where you are coming from. Ultimately I can only point you in the "right" direction but the decisions are yours to make. After all it'll be you using this stuff and not me.
I don't really know what would be the cheapest you could get any of this stuff in the US, but I'd think it should squeeze into the $300 mark.
As for the Fiio E5 it's largely just a toy. It has a nice bass boot feature but besides that you are probably reducing the SQ of most sources by adding one.
Hopefully you'll get some more opinions other than just me...
Just be warned, you will come up with more and more options so if you keep coming back to anything, you should probably just get it. People can suggest new things till the cows come home and it can all get a bit confusing. Try not to get bogged down