A 3 mile commute can be done on literally anything. I would say look for something used on craigslist that is in working order, cheap, and fits you. Then, if you start to like biking (I got into biking from commuting to school), then, you put some money into a bike you really like.

Btw, that Wallyworld road bike actually has STI shifters(!), making it better than the infamous GMC Denali. A guy in the road cycling forum was using the Denali to commute, but he had some mechanical knowledge to fix the assembly errors.