I see this is a month old. But I thought it deserved an answer. I cannot say if the Alesis Multimix is good. However, concerning mics, I think everyone's first mic should be a Shure SM57 or SM58. The 57 is for instruments generally and the 58 is for vocals but they aren't very different. It's been an industry standard for years and it's the cheapest pro-quality mic you can buy. I think they go for $90-$100. Most engineers and musicians I know own more than 3 of these mics. You'll never get rid of it for something better.
Also I think you would receive more responses if you posted in this area:
Low End Theory
It's an area for small budget recording...
Hope this helps.