
Why is Qf3 the best move here for white?


White is down a pawn and poorly developed. Just losing unless white can quickly exert pressure/mount an attack against black's king in the center. White has no natural way to develop the rest of his pieces and build an attack. Nc3 is obviously awful as nxn forces a queen trade and white's bishop has no natural developments either. If b4, be7, bb2, bf6 and black is trading pieces and looking like he might just be up a pawn. Qf3 gains time by attacking the fpawn and opens d1 for the rook which is significant given that is where black's queen and king are lined up. Black does not have time for f6 ... white plays nc3 which is the start of an attack that wins material. Nc3 is also just winning if black tries to guard the pawn with qe7. Both wins are very instructive to review with computer if you don't understand them! So Black is basically forced to play ke8, making it hard for black to finish development. White has compensation for the pawn but there is no forced win -- computer likes nc3, but I might play nd2 which is also decent.

What makes you think that Qf3 is the best move? It isn't so clear to me that it is better than Nd2 (planning Nc4 or Ne4).

1.Qf3 prepares Rd1 that pins the knight and after this move Bf4 and Nc3 both are possible.
This moves are not possible in the start position and that the move is with an attack on pawn f7 is extra nice. It wins a tempo too.