The side streets would be better, in my opinion, IF they are through-roads. Here in my area, though, the major roads go through, and the side streets don't, so you wouldn't have too much choice. Riding around the local neighborhoods, I've never had problems with cars backing out, etc. Of course, I'm going 15 mph and not 25 mph, too.

For 3 miles, I'd wear work clothes if I didn't get them totally sweaty -depends on your fitness and the weather.

Edit: Just noticed you're in Loveland- street clothes should be fine there! We lived in Loveland one year, Fort Collins for 4 years- great riding weather in the summer.