First, ask yourself why an EPS from Photoshop? Is EPS really needed? There was a time where EPS was mandatory if you needed to include clipping paths or other elements. That's not really true today. Many formats today now support what EPS was used for. PDF, PSD, TIFF can all include clipping paths and transparency. PDF and PSD can include spot color channels and vector data, etc. EPS isn't a bad format by any means, but where it was once the go-to for many images, it's needed far, far less today. EPS is a flat-file format, meaning it flattens transparency. Other formats such as PDF and PSD do not do any flattening. EPS files from Photoshop are generally larger in terms of KB and offer less inter-application options today.
Realize an EPS saved from Photoshop always includes raster data. It may or may not include vector data (based upon image content). There is no way to save a purely vector EPS files from Photoshop. None. At best, all Photoshop EPS files are a mix of raster and vector data. THis question may be helpful:
The Preview option sets how you want the low resolution preview image to be formatted. Most EPS files contain an embedded low resolution "proxy" image which is used to display the image as a whole when "placed' or viewed from within some other application.
Choosing None obviously dumps the preview image entirely and you won't see it. In these cases you generally see text such as "This image was created by XXXX and does not contain a preview."
TIFF (1 bit/pixel) is similar to a GIF or PNG8 images in that the preview image for the EPS will only have transparency on or off, there will be no subtle fades to transparent. Every transparent area will be a hard edge.
TIFF (8 bits/pixel) is similar to PNG24 or PNG32 images. This preview format allows the preview image to have 8 bits for transparency which then allows for subtle transitions (fade) to transparent within the preview image.
The above options only effect the embedded preview image and do not actually alter the EPS data within the file. Upon output to a printing device, these preview setting are completely ignored and the internal EPS data is rendered.
DCS (Document Color Separations) is a format based upon EPS. DCS was created by Quark, in the late 1980s/early 1990s, to allow EPS files to separate properly when placed into their QuarkXpress application.
DCS 1.0 was a format which generated 5 separate files. One for each color plate (CMYK) and a composite EPS file for placement purposes.
DCS 2.0, as indicated, was an "update" the the DCS format which allowed the option of generating separate files or generating one single file containing all the separation data. DCS 2.0 also added the ability to include additional color plates. So, DCS 2.0 is not restricted to only CMYK colors. DCS 2.0 is still required today if you wish to use Spot Color channels in a Photoshop-generated EPS file which will be used in QuarkXpress.
In short, if you are not using QuarkXpress, there may be very little reason to ever use the DCS format. It's was specifically designed by Quark for Quark applications.
As for the data encodings:
ASCII/ASCII85 are designed for Windows
Binary was designed for Macintosh. Some applications may have issues reading binary data however.
JPG uses a lossy data encoding which strips away some data. The amount of data removal depends upon the selection fro the JPG format. Here, JPG refers to how the data is encoded and not the image format specifically.
In today's world, simply leaving the encoding on the default ASCII85 is fine across platforms and for most applications. There's no real need to alter the encoding unless you specifically know why you need to (someone requests Binary or JPG encoding). It is not unheard of get a request for Binary data encoded EPS files.
Include Halftone Transfer allows Photoshop to dictate how halftones are created. The Halftone transfer controls how halftone dots are dispersed. This "bakes in" these setting internally within the EPS file. Often it is much wiser to allow the output device to control half-toning rather than setting it in stone within the file. This is generally something you do not want to include unless you are in a pre-press environment and know you need this function.
Include Transfer Function allows Photoshop to dictate the output levels of the file for a specific output device. Basically, what this does is adjust the image levels or curves within the file itself based upon the specified output device. This is also something you do not want checked in most situations. By leaving it unchecked you allow the image to be adjusted upon output by the output device rather than "baking in" these adjustments.
Postscript Color Management is exactly that, color management. If you tick this box, color profiles are embedded into the EPS data. Postscript color management only works with Postscript Level 3. If in a postscript Level 2 environment, this box has no effect. Whether or not you want the EPS color managed within the file is your choice. By not checking this option, you allow the output application to color manage the EPS file. Often this is a more preferred method so in many cases it is suggested you not check this option either.
The above 3 options are really "specialized" options which should only ever be "on" unless you specifically understand why you've turned them on.
Include Vector Data does just that. If you have live type, or shape/vector layers, vector smart objects, etc. then you want this option checked. If you leave this option unchecked, then all vector data is rasterized within the EPS file.
Image Interpolation anti-aliases the low resolution preview image which is embedded within the EPS format. This low resolution preview image is what you see when you "place" the EPS file into other applications. Checking this option can often be helpful, especially if your EPS file contains a great deal of vector data. Whether or not this is checked has no real technical benefit beyond the preview that you, the user, sees when viewing the EPS in some other application digitally.