Here are my opinions on the various colors. Keep in mind, color is an incredibly subjective thing, so take everything I say with a grain of salt. I've seen cars in each of these colors that look stunning, so part of it is what you decide to do with it.
Melbourne red: A very nice color, especially with black accents, like dark tinted windows. I like that it's one of the few standout colors that BMW offers for the M3. A little too much orange for my taste, especially in bright sun light. Wish they had offered Imola instead. If you're interested in this color, be sure to check it out in different lighting situations. Traditionally an M-exclusive color, but I think they're offering it on the iS cars now.
Space Gray: Slightly lighter than silver gray for the E46, but the difference is hard to notice. Hides the dirt very well, but on the other hand doesn't really "pop" when it's clean. A few cosmetic mods can really help in this regard though and make it look sharp. Probably my second favorite color. Not an M-exlcusive color.
Alpine White: It's a good looking color on this car, but it's a little played out. I believe polls over on m3post show that almost 1 out of every 3 M3s is white. Also, if you're interested in modding it, there's not very many directions to take it (everyone seems to do the obvious black on white), so again, it's hard to make it stand out. Compared to Brilliant White (individual color) and the other metallic colors, Alpine White can look a little dull, especially when a little dirty, but when clean is pretty sharp. It is not an M-exclusive color.
Silverstone II: Don't be fooled into thinking this is a traditional silver. It has a very strong bluish hue to it. It can almost look baby blue in some lights. It's much lighter in tone than space gray. A Silverstone E90 M3 parks in my garage at work, and I can't really get myself to like it. It's a very bleh color to me, and probably my least favorite of all the available colors. It is an M-exclusive color.
Jet Black: I don't like it quite as much as Black Sapphire Metallic, which is deeper and glossier, but Jet Black is still an amazing color when clean. Simple, aggressive, and sharp. We all know what black looks like; not much needs to be said here. It is not an M-exclusive color.
Jerez Black: This color is pretty amazing. In some lights it looks very similar to Black Sapphire Metallic; and in other lights it looks like a dark blue. What it lacks in the sharp aggressiveness of Jet Black, it makes up for in depth and personality. To get a feel for what a chameleon this car is, be sure to check it out in different lighting situations. The only thing to be careful of is if you want to go with a "murdered" all-black kind of look. Jerez Black doesn't pull this look off quite as well as Jet Black, thanks to the bluish hint in direct sunlight. It is an M-exclusive color.
Interlagos Blue: This is hands down my favorite color. I never even considered it when I first placed my order, and I hadn't seen it in person. I was driving past my local dealer one day, and there was an IB E92 M3 sitting there and it made my jaw drop. It's one of the few M colors that really has a personality and really stands out. It gets complimented more than anything else about my car. It's a darker color than LeMans Blue, and also has more of a purple hue, especially in bright light. This gives it a little flash or pizazz in direct sunlight, but it's a chameleon, and looks dark and menacing at night. This color probably changes more with the lighting than any of the other colors, so be sure to check it out in different lighting situations. It really looks like two different colors in day and night. It's a tough color to keep clean. Not as bad as black, but no where near as easy as space gray. It is an M-exclusive color.
LeMans Blue: LMB is much more of a "true" blue. It's a great color and nice and rich. It's not nearly as much of a chameleon as Interlagos and IMO doesn't pop as much as Interlagos, but if you want more of a classy, understated look, this is the way to go. It is not an M-exclusive color.