Upgrading an old Trek
The derailleur specs you have to consider are:


Max sprocket size
Min sprocket size
Total tooth capacity 


If you want to go to a 11-28 cassette from 14-30, max sprocket size is ok. 11 tooth min sprocket may be too small. Capacity is also increased by 1. 

11-28 may work but 12-28 is safer. 

6, 7 and 8 speed systems use the same sprocket spacing and progressively wider stacks of sprockets. The other thing you will need to check is the lateral range if both the derailleur and shifter. It may not be enough to cover 7 sprockets.