The Fiio L6 will work great, and Fiio products are very good generally. The E5 is OK, esp for the small price, but the E11 is a good bit better -- cleaner sounding and more powerful if you have a pair of high impedence headphones that need some power.
OTOH, the E7 can be used as an amp from the Fuze, or it can be used as a digital-to-analog converter (DAC) from a computer via the USB. When you plug a DAC into a computer, it is recoginized as a DAC and the sound output is sent out the USB port/cable. I had an E7, and didn't see the need for the DAC option (my computer has pretty good audio processing), and the amp section is not as strong as the E11, so the E7 wasn't much use to me.
There are a number of nice portable amps under $100 (either new or used) that you could try. They all do similar, and TBH you have to have pretty good ears to hear big differences between one and another. IMO, the E11 is a great bargain for it's price if all you need is a portable amp. It has a couple of levels of bass boost if you need/want that, and a very clean sound.
Check out the Pictures of your Port. Rig thread to see tons of examples of player + amp combos.