I'm looking for a bicycle to commute to work (<2 miles), do groceries (~2-3 miles), go to school (~8 miles). Would this be a good bike for that? (one of the cheapest bikes on bikesdirect.com)
While the comments on your question are good, i'll answer anyway.
Short answer: Yes for your specific needs this is a fitting bike. Longer. Yes, If you have some hills, the 3 speed oxford model may help.
Buying a used bike off craigslist for someone with little bike knowledge is probably not a great idea. a $50 - 100 bike in my area is generally pretty old. beat up and not worth the savings.