1) Remote responsiveness can depend on the game. Some pick up your movements incredibly well and some are terrible at it. IGN reviews in particular have been helpful in determining which games are more responsive and which are the arm-flailing equivalent of button-mashing. A remote add-on called Wii Motion Plus is due out this year which should make many games even more responsive (although shovelware will continue to suck).
2) Based on the games you reference, you probably would enjoy Resident Evil 4, Metroid 3, MadWorld, and others along those lines (I am not any good at those so the others on the board will have to advise you on that). It is a relatively common complaint that despite a few good M-for-Mature titles, there isn't yet a big selection of them for the Wii. However, the new control styles have made for some very innovative games that may not be violent but are fun for adults (Boom Blox and De Blob come to mind). Just because a game isn't violent doesn't mean it has to be Party Babyz. Though there sure are a lot of dumb kids games to wade through to get to the good ones.
3) I do like the arcade-style light gun shooting for the Wii. I'm a big fan of rail shooters rather than FPS though, so all I can tell you is that House of the Dead: Overkill and Resident Evil: Umbrella Chronicles are SO FUN (the Link's Target Practice game that comes with the Wii Zapper also kept me entranced for weeks but I can't even tell you why - it doesn't SEEM exciting but it's hard to put down). Some of the more complex FPS style games require using the buttons on top of the remote, rather than just the trigger on the underside. If you're not using a snap-on gun attachment, that wouldn't matter anyway.
If you're more interested in a wide range of "adult" titles and aren't totally sold on the Wii remote motion concept, you might be happier with an Xbox360. We have both, and my husband generally plays with the 360 a lot more than the Wii (I play the Wii a lot, but I'm not what they call a "hardcore gamer"). Graphics are better and there are a lot of titles that he's pretty fired up about. I'm happy to let him play "my" Wii (lol) but there just aren't any games that he cares about.