The truth is, that all the openings have deep and complicated theory. Even the relatively "older" openings such as the Evans Gambit, Italian Game or Three Knights Game had their theory developed really deep in the 18th, 19th and early 20th centuries. But luckily there are openings that are relatively sound. But they are rare nowadays, so by learning the basics of such openings you can go well against the opponents who didn't learn these openings.

What I use:

**White**

1. Vienna Game
2. Italian Game
3. Three Knights Game 1 e4 e5 2 Nf3 Nc6 3 Nc3

The vast majority of your opponents after 1. e4 e5 would expect the Ruy Lopez, so many are not ready for the good old Italian or Three Knights. Of course, these openings are not as good for White as the Ruy Lopez and Black if they play 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 face the Russian game [Petrov's Defence, 1 e4 e5 2 Nf3 Nf6].

Against the Sicilian I play 1. e4 c5 2. c3 [the Alapin Variation]. A sound and good variation that is not that complicated as the main lines of the Sicilian. Also it can often end up as the Advance Variation of the French Defense (1. e4 e6 2. d4 d5 3. e5 c5). [1 e4 c5 2 c3 e6 3 d4 d5 4 e5 transposes to the position after 1 e4 e6 2 d4 d5 3 e5 c5 4 c3 in the French Defence, Advance Variation]

Against the French Defense I play the just mentioned above Advance Variation. This allows me to feel comfortable in both variations as they can be very much alike.

Against the Caro-Kann I play 1. e4 c6 2. d4 d5 3. exd5 cxd5 4. c4. Panov's Attack. This 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 the Sicilian Defence, Sveshnikov Variation [1 e4 c5 2 Nf3 Nc6 3 d4 cxd4 4 Nxd4 Nf6 5 Nc3 e5], though it is far from being "not deep" :)

Against d4 I like using the Volga gambit [the Benko Gambit, 1 d4 Nf6 2 c4 c5 3 d5 b5]. You sacrifice a pawn but get 2 open lines for your rooks 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 the Caro-Kann, or the 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 the Vienna Game, Sveshnikov variation or Three Knights Game. 

Good luck!