Direct mount rear derailleurs are usually nicer and appear on nicer bikes. You really need to find out your size.
Here are some nicer bikes

About the same size as the Shogun. Alu/Carbon KHS Flite for $795
KHS FLITE 720, 56cm

A hair smaller than that Shogun. Cromo mixte Miyata for $140
Miyata 1024 Women's Bicycle

Considerably smaller than the Shogun, a bit smaller than that Miyata, probably. 531 tubing Trek 400t for $395 obo
Trek 400T Elance! --$375 obo

The Trek is my favorite frame of the three, if it fits.