An 11T top gear is a pretty stiff row, unless your big chainring is a 50T. When I was riding a lot, I seldom pushed the 12T top cog on on 7-speed cassettes. A 14T was more to my liking with a 52Tor 53T. I took the 12-28 cassettes off my bikes and usually sported 14-28, although I'm running 13-28 on a lot of my 8-speed bikes now.

A 7 speed Shimano freewheel should go right on your existing rear wheel. Then all you need to get is 7-9 speed Shimano rear derailleur, and a set of 7-speed brifters, or some indexed downtube 7-speed shifters.