I think you're OK to get started. My rule of thumb is that you should aim for a range of 20 at the low to 100 at the top on a touring bike.

At this point what is limiting your range is the freewheel in back -- the spread of 14-28 isn't helping you. If you could get a freewheel with a spread of 12 to 30 or 12 to 32 you'd be fine.