Depends on the dorm; they all have different characteristics. One thing I will say about the dorms is pay attention to your bathroom orientation. Community bathrooms give you less privacy, but it's always cleaned for you (I lived in a dorm with community bathrooms). Suite-style bathrooms are more private, but it's one toilet and one shower for four people, and you clean it yourself.
You can sign up to go in with someone you know, yes. Other than that, you can go in blind, which is pretty random, but I got lucky both years and had some pretty good roommates.
"MSUís masterís program in social work was ranked among the top 25 in the nation by TheBestSchools.org, an independent organization that focuses its ranking system on three criteria: academic excellence, return on investment, and benefits that affect quality of life during studies." -MSU's Rankings and Recognitions page
I wouldn't honestly know about social work, as it's not my major, and I don't have any friends majoring in social work. I will say MSU is a pretty awesome place to be socially and academically IF you're willing to be proactive about things. Go talk to your professors, get to know them, see where it takes you and what opportunities it gives you.