It looks like it's a 7 speed, there are 6 clicks of the derailleur. So now the question is do I just upgrade to a 7 speed freewheel or find a set of 700c rims and go for a 7 speed cassette? Obviously the former is the cheaper upgrade but tire options are limited on the 27" rims.

On a side note the chain rubs on the front derailleur when in the smallest gear in the back, anything I can do there?