Well there's almost no opening you can play like that against e4, but the closest by elimination is caro kann. Reasoning is as follows
Open games - too many semi sound gambits
Sicilian - Immense theory
French - can get very strategically complex and sharp
The other defenses against e4 like pirc, modern are not in the best theoretical shape, plus hypermodern openings arent generally "solid" so I recommend staying away for now.
The caro kann is solid enough and not uber theoretical, if you know how to pick your lines, for eg
the classical with Nc3,play the tartakower with exf6, its actually hard to take advantage of black's doubled pawns and black gets simple development and fairly active pieces. This is a somewhat modern approach so check out Alireza's games in this line.
The advance, play the botvinnik Carls attack defense, if white takes and tries to hold on the pawn too hard which often happens OTB, you will end up with an objectively better position where you will mostly have the bishop pair and a strong centre and can recover the pawn later.
The exchange caro, Learn about the Carlsbad structure and the queen side minority attack. Look at Kasparov's QGD exchange games to understand your play.
For the Panov attack, learn about how to play against an IQP, watch karpovs games, for learning the caro as a whole and for playing against IQP, especially his matches against korchnoi, he often tortured Korchnoi in worse endgames because Korchnoi was fond of playing with an IQP.
This covers more or less any critical tries by white, best of luck.