The idea behind the opening is that white sacrifices a Pawn for quick development in the hopes of launching an attack against back's King. Black can decline the gambit with 2...d6, transposing to the Balogh Defense, but accepting the pawn with 2...fxe4 is considered stronger.
The database of my games has 10 games in which the Staunton Gambit was played. I was white in 4 of them and scored three wins and a draw; playing black, I scored 3 wins, a loss and a draw. Thus, in the ten Staunton Gambits that I was involved in white scored +4 -3 =2.
That's not the statistical results of the games in the 8-million game database, but then these games were played by average players, so maybe the Staunton Gambit is worth a try if you are an average player! It also suggests that you should not expect a lot of draws.
In 1908 Frank Marshal and Rudolf Spielmann met three times in tournaments: Prague (Marshall won), Vienna (Spielmann won) and at Dusseldorf where Marshall handed Spielmann a quick defeat using the Staunon Gambit.
Frank Marshall–Rudolf Spielmann16th DSB Congress, Dusseldorf08.10.1908Stockfish 15
Dutch Defense: Staunton Gambit 1.d4 f5 2.e4 fxe4 3.c3 3.f3 This is a
rarely played, and risky, sideline. d5 4.fxe4 dxe4 5.c4 f6 6.g5 c6 7.d5 g4 8.e2 a5 9.b5+ d7 10.bc3 xb5 11.xb5 c6 12.dxc6 xc6 13.ec3 After this white's position deteriorates. a6 14.a3 b5 15.xf6 exf6 16.d5 xa3 17.bxa3 a5+ 18.f2 0-0 19.f1 ad8 20.h5 d2+ 0-1 Anon-Tartajubow,
Correspondence 2009 3...f6 4.g5 c6 4...g6 Seldom played but it turns
out to be the favorite of no less a player than Stockfish! My opponent was
years ahead of his time. 5.f3 exf3 6.xf3 d5 7.d3 g4 8.h3 xf3 9.xf3 c6 White should have started operations on the K-side with 9.h4 10.0-0-0 g7 11.de1 bd7 12.hf1 0-0 The position is equal, but white eventually won in
Tartajubow-Anon, 1967 5.f3 exf3 6.xf3 e6 6...d5 7.d3 g6 8.e5 b6 9.e2 xb2 Bad...very bad. He should have played 9...Bg7 10.0-0 xc3 11.xf6 and white soon won. Lalic,B (2590) -Kovacevic,V (2520) Slavonski Brod 1995 7.d3 e7 At this time this position was known from Lasker,
E-Pillsbury,H Paris 1900. Lasker won with 9.Ne5, but Marshall's move is
equally good. Stockfish already gives white a winning advantage! Where did
black go wrong?! 8.0-0 White has a decisive advantage. 8.e5 0-0 9.xf6 xf6 10.h5 g6 11.xg6 e8 12.xe7+ xe7 13.0-0-0 White has a decisive
advantage, but it took Lasker 80 moves to demonstrate it. Lasker, E-Pillsbury,
H Paris 1900 8.e2 This is less effective. 0-0 9.0-0 c5 10.e4
White is much better, but in Zavadil,M (2138)-Macicek,J (2056) Frydek Mistek
2007, he managed to lose the game. It demonstrates how slippery a slope the
Staunton is for the non-master. 8...d6 No N on e5 for white! 9.e2 a6 10.a3 Prevents Nb4 and leaves the N misplaced. c7 11.ae1 In his book,
My Fifty Years of Chess, Marshall wrote that he believed Spielmann was simply
"afraid to castle", adding that it was the only good move as he is preparing
Nh4 followed by Bxf6 and Qh5+. b6 Sad to say, this is probably as good a
move as any. 11...0-0 is, however, very little help. 12.f2 d7 13.h4 f7 14.e2 g6 15.h6 h5 16.g5 Black is facing a very dangerous attack.
One possibility... xf1+ 17.xf1 e5 18.f7 e4 19.xe4 e8 20.xh7
with a decisive advantage. 12.h4 d7 This is the worst possible move, but
he had to make a move. 12...0-0 13.e4 xe4 14.xe4 xf1+ 15.xf1 g6 16.xg6 xg5 17.e5 e7 18.f7 and there is no satisfactory way to meet the
threat of Qxh7+ 12...d7 is refuted by 13.xf6 xf6 14.h5+ f8
White has two winning lines: 15.Ne4 (objectively the strongest) and 15.Rxf6+
(the prettiest). 15.xf6+ gxf6 16.xh7 e7 16...e5 17.h6+ f7 18.e4 e6 19.g6+ e7 20.g7+ f7 21.g6+ e6 22.f4+ e7 22...exf4 23.xf6# 23.dxe5 fxe5 24.g6+ d7 25.xh8 and wins 17.g6+ 13.f5 f8 13...exf5 14.xf5+ e8 15.xc8 xc8 16.xf6 gxf6 17.xf6 f8 18.xe7 d7 18...xe7 19.xe7# 19.h5+ f7 20.xd6+ e6 21.e5 d8 22.e4 f8 23.f6 e6 24.xe6 xe6 25.xe6 Black can only avoid Re8# by giving up the
exchange. 14.xe7 xe7 15.e4 f8 16.xf6+ gxf6 17.f3 This has a
surprising tactical flaw. 17.f2 was correct. f7 Getting away from
white's R 17...e8 18.xe6 xe6 19.f5 18.h6 was very strong. a6 17...e8 After this black's hopes of saving the game drop to
zero. 17...a6 This at least would have allowed black to continue playing. 18.h6 18.xf6 xd3 19.xe7 xf3 20.xf3 xc2 white is only slightly
better. 18...f7 19.c4 g8 White is better, but there is no forced win
and so black can continue to put up a fight. 18.xe6 Easy ti see, but nice
anyway. It's hard to believe Spielmann missed this...or perhaps he just
decided to end it, but then why not resign? f7 18...xe6 19.f5 19.e4
The h-Pawn is the next target. b7 20.h4 g7 21.xh7 h8 22.h3+ Black gave up 22.h3+ c7 23.xf6 e7 24.g6 xh7 25.xh7 and there is
nothing black can do. 
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