The E7 is good at driving low-impedance headphones, but if you need more power, you'd couple the E7 and E9 together. You can read up on both components in this thread:
http://www.head-fi.org/t/554593/does-anyone-own-the-fiio-e7-and-e9
Fiio reportedly has a good price-performance ratio. I have no experience with the gear, so I can't say whether you'll be happy with the setup or not.
Correct, you can take the E7 with you as a portable external sound card, and the E7 will perform better than any onboard sound you'll have on most any notebook. If you go for the Fiio setup, you should just start with the E7, see if that satisfies your needs, and if not, get the E9 too.
I'd recommend looking at reviews for the Fiio vs the HeadAmp pico Slim. Both get great reviews:
http://www.headamp.com/pico/pico_slim_amp/index.htm
There are probably a few more options around, but anything you see get frequently discussed here probably is an able performer, and it comes down to taste. If you definitely need a mobile amp, go for the Fiio or HeadAmp. If you're only looking for something stationary, check out Schiit.







