Padel is always played as doubles, so choosing a side is an early decision to make with your partner (preferably before you get to the court). There are different characteristics for each side, which can also change if you and your partner are left or right handed. As left handers are the minority, they almost always play in the preferred position on the right side of the court. This means the balls down the centre of the court would be their forehand or smash side.
Right handers as the majority would have to select which side they should play on, so here are the options for the different sides:
Players on the right side of the court are usually more consistent and their job is to set the point up for the player on the left to finish. This is the traditional view, but now as the level of play improves, players can dictate the game from both sides, there are many examples of both.
Players on the left side are usually the more aggressive and athletic, as it is their responsibility to cover the lobs that go into the middle of the court. It is much more advantageous for the left side player to hit a bandeja than for the right side player to play a high backhand volley.
One of the biggest mistakes for new players is to select a side too early in their padel journey. I regularly see beginners insist they play a particular side when they have not experienced enough padel to understand the game. Playing one side gives you a much better understanding of how to play the other. Even if you want to play the left side, it is worth you experiencing the right side, so you know what your partner is looking for. You even see the top professionals switching sides depending on who they play with, so do not feel like you need to stick to one side.
Conclusion: Do NOT choose your side too early, get plenty of experience on both sides before you do!