Asteroids can be found in virtually every system, and larger systems can contain asteroid belts. 95% of the time, asteroids are irrelevant. Because each asteroid contains only a single resource, mining them is less efficient than mining a planet with several. However, because asteroid belts contain a LOT of asteroids, several of them are bound to be very rich (having a high resource percentage value, which controls resources mined per tick). If your empire has a shortage of steel, lead, etc. in you home system, you can find a rich asteroid - by going to the Expansion Planner and checking the "show asteroids" option - to supplement your supplies.
The Hidden Rock is a special asteroid that will increase the revenue of a resort base built at it. (as opposed to building a resort base at any random location) The same is also true of the scenic bonus you mentioned. To easily see all good candidates for resort bases and how much of a bonus each provides, hit the "potential resort locations" button on the left side of your screen, one of the transparent buttons just above the bottom left info box.
I don't have much experience with missiles; I tried them once in the early game, intending to use my weak ships to kite the pirates. I found that I had a lot of trouble making a ship that could outrun the pirates with my inferior tech, and that they didn't afford my spaceport the firepower to deter much. I just use beam weapons, as their general battle strategy is simple and effective: get on top of bad guys -> melt their hulls into globs of floating metal.
I also don't have much experience with gravitic weapons. Early on, I find their short range and low fire rate, combined with the fact I can only fit a few of them, to be very underwhelming. Later on, though, I can see a fleet with ships large enough to hold a decent number of longer-ranged gravitic weapons being a scary force indeed. Trying to fight a powerful pirate faction armed with them is certainly proving challenging. =P
< Message edited by Starke -- 7/14/2013 8:26:03 AM >