Below it is a list of the optimal moves that a second player can make in order to avoid losing (all represent a tie when played optimally), after each possible first move. All the other moves can result in a loss for the second player.
a b c a b c a b c
─────────── ─────────── ───────────
1 │ 1 │ │ │ 1 │ 2 │ 1 │ 2 │ 1 │ │ │ 1 │
│───────────│ │───────────│ │───────────│
2 │ │ 2 │ │ 2 │ │ 2 │ │ 2 │ │ 2 │ │
│───────────│ │───────────│ │───────────│
3 │ │ │ │ 3 │ │ 2 │ │ 3 │ │ │ │
─────────── ─────────── ───────────
a b c a b c a b c
─────────── ─────────── ───────────
1 │ 2 │ │ │ 1 │ 2 │ │ 2 │ 1 │ │ │ 2 │
│───────────│ │───────────│ │───────────│
2 │ 1 │ 2 │ 2 │ 2 │ │ 1 │ │ 2 │ 2 │ 2 │ 1 │
│───────────│ │───────────│ │───────────│
3 │ 2 │ │ │ 3 │ 2 │ │ 2 │ 3 │ │ │ 2 │
─────────── ─────────── ───────────
a b c a b c a b c
─────────── ─────────── ───────────
1 │ │ │ │ 1 │ │ 2 │ │ 1 │ │ │ │
│───────────│ │───────────│ │───────────│
2 │ │ 2 │ │ 2 │ │ 2 │ │ 2 │ │ 2 │ │
│───────────│ │───────────│ │───────────│
3 │ 1 │ │ │ 3 │ 2 │ 1 │ 2 │ 3 │ │ │ 1 │
─────────── ─────────── ───────────
From the above scheme, we can choose from standard opening moves, since there is no such big difference between them:
Since no second move is a certain win for the second player, it follows that the first player is guaranteed a tie for any move that it makes. So, choosing the first move is not that important, but, since it is intuitively better to constraint the opponent's moves, a good first choice would be one of the corners, since the second player can only choose the center of the board in order not to loose.
If the player is second, it should choose one of the moves that guarantee a tie. From the above figures, it appears that a general rule is to choose the center of the board, except when it is already chosen, in which case it should choose any corner.