Which 3D printer should I use to make custom miniatures for a tabletop game? I would also be curious on how I could get the best results with these printers. I am in a situation where I have cheap access to a:

Fortus 250mc, which prints in ABS and has a minimum resolution of 0.007mm (but that can be raised as high as 0.013mm to print faster), and has a "Soluble Support System" which enables printing overhangs. 

Form 2, which prints with Photosensitive Resin, has a resolution of .05mm, and can also print overhangs. 

Stratasys Dimension SST1200es, prints in "ABSplus" (whatever that is), has a resolution of .254 mm, and can indeed print overhangs. As far as I can tell the main advantage of this one over the Fortus is that the supports can be immediately removed after printing and don't need to be dissolved first.

I am okay with processing or finishing the miniatures later so long as it's not too time consuming (such as by running an acetone vapor bath), but I'm curious when I would use each printer and how I could get the most out of both. 

P.S. Also the Stratasys is more expensive for me to print on than any of the others so please keep that in mind when answering :)
The Form 2 will definitely give the best results for your application.

Both the Fortus and the Dimension use FDM, which builds the model up using a bead of molten plastic. Because this bead is typically 0.5mm in diameter, this strongly limits the details you can print.

The Form 2 uses liquid resin, that is cured by scanning it with a laser. This process is called SLA. The laser produces a 0.14mm dot, and so you can produce much finer details. The Form 2 can also use much thinner layers (down to 0.025mm v.s. the 0.178mm of the Fortus) so the models will be much smoother.

To make small miniatures SLA is much more suitable than FDM.