I agree that I don't see a need for "suspension" unless your are mountain biking. if you are a new rider then you should visit some bike shops and do some test rides, maybe even rent a bike for a day or two. some folks like drop bars for commuting (I do) but others who live in the city and do urban commuting prefer straight bars which can be found on straight bar road bikes or sporty hybrids (not comfort bikes). also, if you are a new rider your preferences are likely to change after you do some commuting for a while so it might be wise to get a used bike to start with. I started with a mountain bike; then mistakenly changed to a hybrid; roadified that hybrid with drop bars and high pressure tires and a road saddle before settling in with a standard road bike.
but at 6 miles each way it almost doesn't matter what you ride because the ride will be over so quickly. regional bike availability may be more relevant. meaning: what bike can you get your hands on quickly and cheaply. lot's of folks here have more than one bike and it's because their preferences changed the more they rode. I have 4.