I just use a cheapo 7-speed Next bicycle I bought from Walmart.com and had shipped to my house for free. Total cost: $95 on sale. The distances I travel by bicycle are similar to what you describe, so really it doesn't make much of a difference. I did, however, also buy "Essential Bicycle Maintenance & Repair" on BN.com which is very helpful for taking care of my bicycle by myself. No need for a bike shop once I bought a few essential tools off Amazon to go with it.
Oh, and I highly recommend getting an Aosom bicycle trailer off Amazon to use for grocery/cargo runs. I spent about $60 to buy one with free shipping and no sales tax and it works great.