Dropkick = melee while boosting.
Every weapon is useful, more or less. The least useful is the saw blade, since it's really only good as a melee weapon. The lock-on laser seems bad at first, but it's actually pretty useful in certain situations. It kills regular grunt enemies in 1 or 2 shots, and you can lock-on and blind fire as you're running somewhere, so you don't even need to aim. I think the higher the difficulty you play on, the more useful it becomes. I never used it much on normal, but on God Hard I usually picked it up when I came across it. The LFE gun seems kinda crappy at first, but it's pretty good for clearing some space. If you've got a bunch of romanovs coming after you, and you have no shields, you can just blase them with the LFE and it'll send them flying, giving you time to recover. The sniper kinda sucks too, but again, on the higher difficulties it can kill any grunt enemy with one headshot, which can be very useful in certain fights. The AR, HMG, shotgun, and rocket are awesome of course. The AR is the best all-around weapon in the game.
Nothing in the stats screen affects your score except for how many times you die (-1000 points for each death I think) and how quickly you beat it.
Forgot to mention, you can 'backpack' reload your weapons, in case you didn't know. For example, if you're firing the AR, and you start reloading, immediately switch over to the HMG; you'll be able to continue firing uninterrupted as your AR reloads automatically. So you basically never have to wait to reload your weapons in this game.