If we had basic orbital infrastructure, which we will likely have before the end of the century, it isn’t such a daunting task. These lasers would require a lot of energy, but nothing a large solar array or small nuclear reactor couldn’t handle. Sending 3 or 4 of these lasers into orbit around the sun is probably easier than building a solar sail big enough to move a spaceship that can sustain a crew for years. Although both would be huge tasks.
Similar to how a sailboat can sail into the wind, a solar sail can use the sun’s light to slow its orbital velocity, lowering periapsis. It isn’t used only to push directly away from the sun- that wouldn’t be very useful at all.
I think what you are describing is more or less identical to the Hohmann transfer, or more precisely a patched-conic trajectory, as already described by @Stranger_On_A_Train . Things are even worse, though, than that first-order calculation describes because the orbit of Mercury is inclined, as in by a lot, even compared to planets like Mars where orbital inclination is already an issue. In any case, the Venus flyby saves you a huge amount of fuel.
Hohmann orbits are only optimum if you ignore all other objects. In the real Solar System, though, where you do have other objects, you only ever need slightly more than the energy needed to reach the next closest object (in our case, the Moon). Though depending on how much more your “slightly more” is, and when you want to depart, you might end up with an extremely long and complicated path to get there.
One thing about sending humans to Mercury is, the trip has relatively few unknowns. To land anything (manned or unmanned) on Mars, say, you have to go through an atmosphere, and atmospheres can do all sorts of crazy unpredictable things. Mercury doesn’t, though, so you don’t have to worry about that unpredictability.
Ha!!!