Well it seems like your choices are all basically Xenos. Eldar of the good bad variety, tyranids, orks, Tau, necrons, or daemons.
Do you have a "current competitiveness" requirement?
I think if you're just going for stark juxtaposition then I think your best bets are eldar, tyranids, or daemons, with necrons a close fourth.
I wouldn't claim that Daemons are Xenos....
But more to the point...I know I don't want anymore Rhinos (I've got somewhere between 12-14 of them), and I'm not excited about more blocky vehicles, I'm not against Chimeras and the like. I'm just not excited about camo paint jobs. They're not fun in my mind to paint.
I'm not panicking about needing some level of uber-competetive army. I'm actually a pretty solid at playing my Sisters army, I'm just getting rather bored putting the same thing on the table week in and week out. Love the army, hate the inflexibility in the codex (but that's a rant that's well known so I'm going to skip over it). Either way I'm confident that I can learn and tweak an army to play well (assuming I find something I enjoy playing).
Regardless, I'm not against the Imperium as a whole, just against playing your bog standard Marines. With the release of the Pre-Heresy Terminator armor I've kicked around a Pre-Heresy Deathwing army, Gray Knights (with a mix of Terminators and Inquisition (Inquisition provides a fire base to the Terminators ability to punch things in the base to create a purge and hold sort of duality in the army), and Black Tide Templars.
The problem that I've run into is that I don't know a lot about playing or building these armies, much less playing and/or building them in 6th Edition.
TL;DR: I guess the better phrasing of the question would be "In 6th Edition, what is a decent, non-standard army (i.e.: not standard Marines and no Rhinos) that has some fun things to it (and isn't necessarily ultra-competitive) that I could start, and what is the best way to do it?"