I recommend the London system as white for an easy system and the Scandinavian as black against e4 and Kings Indian Defense (KID) against d4.
Of these recommendations I only ever actively played the Scandi so that's all I can really explain in depth. For an easy system I recommend the d8 Scandinavian:
The general plan is to trade off the light squared bishop and then place pawns on c6 and e6 (which control the light squares and blunt White's light squared bishop). Generally it will look something like this:
IM John Bartholomew has some great resources on this opening and it is very playable for players sub GM level.
I have mostly solved puzzles (rating around 2250), never really played chess online seriously. I want to start to play now and need an opening system. I do not want to spend much time on learning opening lines so I want a system that fulfill the following criteria:
a) Is almost the same for white and black
b) Uses the same moves pretty much no matter what opening the opponent plays.
Searching the Internet for openings I have found the following three alternatives. Are they valid and which one do you recommend.
1. Nimzo-Larsen for white - Owen defence for black
2. White hippo - Hippo defence for black
3. Kings Indian attack for white - Kings indian defence for black
Regarding the last alternative, is the kings indian defence a universal opening? For example can it be played against both e4 and d4? (starting with 1..d6 against e4 and then going Nf6) or am I missing something? Is KIA like the KID or does it develop into a different middle game?