QFI is one of those characters where you wish you could store at least a handful of build templates - there's several unique ways to play:
- sabotage sniping with javelin (or whichever SR you prefer), max weapon/SR damage - can get boring unless javelin.
- "ghost" build with duration/bonus power cloak, sabotage and stickies - best with shotguns like the Raider of pistols like the Paladin
- melee build - challenging but fun.
- tech burst build - variant on "ghost" as above however 4 ranks in cloak and take grenade capacity with max stickies for many explosions. I don't like this so much because it's not very elegant - you may as well play the TSab or an engineer if you want to go the all out explosion route, and besides there are already too many classes revolving around explosions in this game.
At the moment I have her specced for "ghost" with Raider and shocktrooper package - essentially a shotgun infiltrator with duration/bonus power and sabotage which makes you almost untouchable. This is the real invisible infiltrator - the shadow has nothing on this because sabotage is awesome for distraction and stickies don't break cloak - so you can pretty much toy with the enemies for the entire match. Melee still hits hard without speccing entirely as a melee build.
Demolisher is an easy one - 4/6/6/4/6 full melee, crusader + omni-blade, strength enhancer and grenade capacity. Essentially batgauntlet "lite" version. Arc grenade -> sprinting heavy melee. Shoot and homing grenades for variety.
Fury is one like you I initially loved when it was released, then hated for a long because it grew incredibly boring, then tried to play melee with her in the past but kind of failed, now have come back to a melee build and it is surprisingly good fun - this is what I play at the moment.
Goes away from the usual adrenaline mod plus throw spam in favour of a (albeit less efficient) multi stringed approach - making use of all offence in equal measure - heavy melee, light melee, shotgun, throw, AF detonation and DC. Cyclonic is preferred because it's a playstyle choice - I like taking it slow and savouring the light/heavy melee and AF detonation so it's nice to tank some hits. And it's a nice change of pace to not run around like a maniac blowing everything up!
Fury is a weird character in terms of playstyle - very easy to create one of the most monotonous yet most destructive builds in the game, but also possible to play slightly less destructive and one of the most varied builds in the game, because light and heavy melee is so awesome to use. Kind of like the Shadow - except with the shadow it is two separate builds whereas with the Fury it is largely one build choice (not counting DC sniping because that is seriously boring - you want to always spec all three powers IMO for most variety and fun). The difficulty is in forcing yourself to choose the suboptimal option during combat - so for example
- heavy melee through wall, detonate AF, finish enemies with light melee and shotgun
- DC, heavy melee in, detonate AF for BE, light melee to mop up, dodge out
I'm struggling to describe it here but it's a conscious choice NOT to use throw in every occasion, but use shotgun (ie wraith), light melee, heavy melee, AF detonation (because AF detonation is FUN!
). You as the player need to create the variety in attacks, which finally seems to be sinking into my awareness. Yes having r6 throw is great for use on say, atlases, for example, and great in a tight situation where having an on demand BE is necessary. But now I find myself shooting and meleeing more than using throw - maybe only using once to soften up a group then going all street fighter on what's left. 
I am by no means speaking with much experience so best to compare with info from more experienced fury players - I had ignored this character for a long long time for aforementioned reasons, only recently clicking with a varied playstyle.