I have been told that it is possible to guarantee no worse than a tie in normal 3x3 tic-tac-toe, but that the first move is very important. What is that important first move?
Tic-tac-toe has been solved. The optimal first move is to go in the corner.
As always, there is a relevant xkcd.
The first move can be made anywhere without sacrificing the game. If the opponent plays perfectly, any first move leads to a draw.
However, if the opponent does not play perfectly, then the optimal place to go is the corner, since that leaves only one spot (the center) for the opponent to go to get a draw, increasing their chance of making a mistake.
If you're first: Go in a corner.
If you're second, and the first person went in a corner: Go in the middle.
From both of these positions, it is possible to guarantee no worse than a tie.
There is a nice article analyzing the Tic Tac Toe first move strategy at https://paperandpencilgames.com/2019/02/tic-tac-toe-strategy-tutorial.html
To address the reviewers comments, here is the conclusion of the article. There is no way of winning against a "perfect player". Choosing a corner as the first move gives you the best chance of winning against a less experienced opponent. Even if your opponent is a "perfect player" you can still tie the game.
One way to answer this is to consider all 255,168 possible games of tic-tac-toe and record if they result in a win, draw or loss for the starting player and analysing where the first move was for each of those games. According to such an analysis, opening in the centre is best, in this case.
Taking it a step further, about 90% of those games are "stupid" because they include moves where players either miss the chance to win immediately or they miss blocking the opponent who can win in their next move. If you disregard those games, then the best opening move becomes a question of how you define "best". If you consider the number of winning games that there are after opening, then an edge opening is best. If you want to avoid drawing or losing, then the center is best. You can combine those results, say weighting winning with a factor of one hundred, drawing with a factor of 10 and losing with a factor of -1. This results in the center again being the best place to start.
In contradiction to most of the answers here, starting in the corner is hence not the best move, when using the number of games that can be played from an opening move as an indicator of what is "best".