+1 on the Tikit, it folds fast, rides well, rolls, is not heavy and can be customized and adapted into whatever you decide you need. It has a lifetime guarantee and you can pass it down to your grandkids. The transit cover is quicker and more practical than a bag. And you will just have fun riding this bike!
if you get a cheapo bike you may find the ride so unbearable that you scrap the whole idea of commuting on a bike...
get a Tikit, (like the seasons Tikit with an internally geared hub), and then add racks, adjustments, schlumpf cranks, dynamo hub + lights, etc. as needed