Don't use eps bitmaps. They come in at low bit rates. Use psd files. EPS is for doing things like vector masking on high rez images for print and for maintaining fonts for printing. They have very little place in video production.
Then, using a Photoshop-formatted (.psd) image, what's the best way to mask/create a clipping path for the image so its background is transparent once it's imported into After Effects? With the EPS format I could use Magic Wand selections, Quick Masking and alpha layers to create a very precise mask, then create a clipping path using that mask and the all areas of the picture in the mask would be transparent when imported into other apps.
All transparency in Photoshop is supported in AE directly except transparency created with this tool in the Effects Panel:
To access this type of blending you need to import with editable blending modes and then enable Use Blend Range from source in the Advanced Blending options under Layer Styles in AE. I actually use this a lot to clean up mattes.
Your workflow is atrocious, to say the least. As Rick suggested, simply use PSDs. AE will perfectly rretain PS' transparency and - surprise, surprise - if you import it as a comp, AE will even convert layer clipping paths to masks.