The truth is, that all the openings have deep and complicated theory. Even the relatively "elder" openings such as Evans gambit, Italian game or 2 Knights Defense used to have their theory to be developed real deep in 18th, 19th and early 20th centuries. But luckily there are openings that are relatively sound, but they are rare nowadays so by learning basics of such openings you can go well against the opponents who didn't learn these opening.

What I use:

**White**

1. Vienna Game
2. Italian Game
3. 2 Knights Defence

The vast majority of your opponents after 1. e4 e5 would expect Ruy Lopez, so many are not ready to old good Italian or 2 Knights. Of course, these openings are not as good for white as Ruy Lopez and Black if plays correctly can have equal chances, but the point is that few people actually know how to play in these openings and I quite often managed to achieve superior positions against much stronger players than I am.

Also when playing 1. e4 you of course should be ready to Russian game.

Against Sicilian I play 1. e4 c5 2. c3. A sound and good variation that is not that complicated as the main lines of Sicilian. Also it can often end up as a classical variation of French defense (1. e4 e6 2. d4 d5 3. e5 c5). 

Against French defense I play just mentioned above classical variation. This allows me to feel comfortable in both variations as they can be very much alike.

Against Karo-Kann I play 1. e4 c6 2. d4 d5 3. ed cd 4. c4. Panov's Attack. Gives white a strong and active position and it is you and not your opponent who chooses the variation, so you don't have to study anything but this variation.

**Black**

Against 1. e4 I always play Sveshnikov variation, though it is far from being "not deep" :)

Against d4 I like using Volga gambit, you sacrifice a pawn but get 2 open lines for your rocks and your queen. In my memory I cannot recall losing a single game in this variation except when I played against IMs and GMs. 

Against c4 I play as was advised above the hedgehog system. Which is also far from being "not deep" :)

So to make a conclusion, I would suggest you to choose variations that you can enforce (such as Panov's Attack in Karo Kann, or Vienna Game after 1.e4 e5). When doing so you limit the number of variations you should learn and you can concentrate on learning them deeply. This will give you a huge advantage over an unprepared opponent especially when an opening is full of tactical tricks and traps such as Vienna Game, Sveshnikov variation or 2 Knights Defense. 

Good luck!