What White moves give away the first-move advantage?
I'll let Stockfish decide it. :-)
Analysis by Stockfish 6: 1. +/= (0.33): 1.e4 e5 2.Nf3 Nc6 3.Bb5 Nf6 4.0-0 a6 5.Bxc6 dxc6 6.Nxe5 Nxe4 7.d3 Nf6 8.Re1 Be7 9.Bg5 0-0 10.Nc3 Bf5 11.h3 Bb4 2. = (0.18): 1.Nf3 d5 2.d4 e6 3.Bf4 Nf6 4.e3 Be7 5.Nbd2 0-0 6.Bd3 Nh5 7.c3 Nxf4 8.exf4 Nc6 9.0-0 Bd7 10.a3 h6 3. = (0.17): 1.d4 Nf6 2.Nf3 e6 3.c4 d5 4.e3 Be7 5.Nc3 0-0 6.Bd3 c5 7.cxd5 cxd4 8.Nxd4 Nxd5 9.0-0 Nc6 10.Nxc6 bxc6 11.Bd2 4. = (0.16): 1.e3 e6 2.Nf3 Nf6 3.c4 Be7 4.Nc3 0-0 5.Be2 d5 6.0-0 c5 7.d4 Nc6 8.Bd2 dxc4 9.dxc5 Qa5 10.Bxc4 Qxc5 5. = (0.15): 1.Nc3 d5 2.d4 Nf6 3.Nf3 Nc6 4.e3 e6 5.Bd3 Be7 6.0-0 0-0 7.Bd2 a6 8.Re1 Bd7 9.a3 h6 10.e4 dxe4 11.Nxe4 Nxe4 12.Rxe4 6. = (0.00): 1.a3 e5 2.c4 Nc6 3.Nc3 Nf6 4.Nf3 Be7 5.e4 d6 6.Be2 Nd4 7.0-0 0-0 8.d3 Bd7 9.Be3 Nxe2+ 10.Qxe2 Ng4 11.Nd5 f5 12.h3 Nxe3 13.Qxe3 7. = (-0.01): 1.c3 d5 2.d4 Bf5 3.Bf4 e6 4.e3 Bd6 5.Bxd6 cxd6 6.Nd2 Nf6 7.Ngf3 0-0 8.Be2 Nbd7 9.0-0 Qb6 10.Qb3 h6 11.Qxb6 8. = (-0.03): 1.c4 e5 2.Nc3 Nf6 3.Nf3 Nc6 4.e3 Bb4 5.Be2 0-0 6.0-0 d6 7.d4 Bf5 8.Bd2 Bxc3 9.Bxc3 Ne4 10.Nd2 Nxc3 11.bxc3 h6 9. = (-0.06): 1.h3 e5 2.e4 Nf6 3.Nc3 Bb4 4.Nf3 0-0 5.Bc4 Nc6 6.0-0 Bxc3 7.dxc3 Nxe4 8.Bd5 Nf6 9.Bxc6 dxc6 10.Nxe5 Bf5 11.Be3 Qxd1 10. = (-0.10): 1.d3 d5 2.Nf3 Nc6 3.d4 Nf6 4.e3 a6 5.Nc3 Bf5 6.Bd3 e6 7.Bd2 Bd6 8.Bxf5 exf5 9.0-0 0-0 10.a3 h6 11.h3 11. = (-0.17): 1.f4 d5 2.Nf3 e6 3.e3 Nf6 4.Be2 Be7 5.d4 0-0 6.0-0 Bd7 7.c4 dxc4 8.Bxc4 c5 9.Nc3 cxd4 10.Nxd4 Nc6 12. = (-0.12): 1.g3 e5 2.Nf3 e4 3.Nh4 d5 4.d3 exd3 5.cxd3 Nc6 6.Bg2 Bc5 7.Qc2 Be7 8.0-0 Nf6 9.Bf4 0-0 10.Nc3 d4 13. = (-0.18): 1.b3 e5 2.e4 Nf6 3.Nc3 Bc5 4.Bd3 d6 5.Nf3 0-0 6.0-0 a6 7.Bb2 Nc6 8.Na4 Ba7 9.Nc3 Bd7 10.Nd5 b5 11.c3 14. = (-0.19): 1.h4 d5 2.d4 c5 3.e3 Nf6 4.Nf3 e6 5.Nc3 Nc6 6.a3 c4 7.Qe2 Be7 8.e4 dxe4 9.Nxe4 0-0 10.Nxf6+ Bxf6 15. = (-0.22): 1.a4 e5 2.e4 Nf6 3.Nf3 Nxe4 4.d3 Nf6 5.Nxe5 Qe7 6.Qe2 d6 7.Nf3 Nc6 8.Nc3 Bd7 9.Bf4 h6 10.h3 0-0-0 11.0-0-0 Kb8 16. =/+ (-0.32): 1.Nh3 e5 2.e3 d5 3.d4 Nc6 4.Bb5 exd4 5.Nf4 Bb4+ 6.c3 dxc3 7.Nxc3 Nge7 8.0-0 Bxc3 9.bxc3 0-0 10.Ba3 Bf5 11.Qa4 17. =/+ (-0.37): 1.Na3 e5 2.e4 Nf6 3.d3 d5 4.exd5 Nxd5 5.Nf3 Nc6 6.Be2 Bc5 7.0-0 0-0 8.Bd2 Bf5 9.Nc4 f6 10.a3 b5 11.Ne3 Nxe3 12.fxe3 18. =/+ (-0.47): 1.b4 Nf6 2.Nf3 e5 3.Nxe5 Bxb4 4.c3 Be7 5.d4 d6 6.Nd3 0-0 7.Nd2 Nc6 8.e3 d5 9.Be2 Ne4 10.Qb3 19. =/+ (-0.42): 1.f3 e5 2.e4 Nc6 3.Ne2 d5 4.exd5 Qxd5 5.Nbc3 Qd8 6.Ng3 a6 7.Bc4 Nf6 8.d3 b5 9.Bb3 Bb4 10.0-0 0-0 11.Nge4 Nxe4 12.Nxe4 Qd4+ 13.Kh1 20. =/+ (-0.69): 1.g4 d5 2.e3 e5 3.Nc3 Nc6 4.Bg2 Be6 5.d4 e4 6.h4 Be7 7.g5 h6 8.f3 exf3 9.Qxf3 hxg5 10.hxg5 Rxh1 11.Bxh1
Firstly, I find it quite silly to copy paste engine evaluation tree as an answer. Engines are not strategists, actually, engines are silly when it comes to strategy, comparing to humans. Therefore, it's wrong to use engine evaluation tree, and it is not a contribution, anybody can copy paste engine output.
As it's a total-beginner question, I would recommend you to go 1.e4 for an open and tactically rich play to improve your game, instead of searching for best opening move(s), because it's not a simple question, actually extremely hard one.
But if you really want an answer, all top-level playable first moves are secure enough to play(so you won't lose your first move advantage). If top level players(black side) can't refute them, your opponents can't refute them too. Including but not limited to these: 1.c4, 1.d4, 1.e4, Nf3, 1.Nc3, 1.g3 etc.
There are two moves I'm quite certain that loses advantage, 1.a4 and 1.h4, which achieves nothing useful, and weakens pawn structure.
Lastly, an opening is strong when the practitioner understands the underlying strategy. So, try to understand the opening(which opening you decide to play), memorizing variations is not enough. Even if you memorize all variations in 10 moves, if you don't get the idea of the opening, you can't put the resulting position to good use.