Opening a photo as 8-bits out of ACR chops off the lower resolution bits. Either you should open the file out of ACR as 16-bit ProPhotoRGB (large colorspace) if you have more processing to do in Photoshop, or as 8-bit sRGB (small colorspace) if you are done toning it in ACR and just need a file to display after doing a few more non-toning-related things in PS.
In short, 16-bit ProPhotoRGB keeps the most color resolution so there is the least degradation when toning the photo, but it cannot be saved as a JPG, so a conversion to 8-bit sRGB usually needs to occur before saving as a JPG.
Some people convert to Adobe RGB instead of sRGB but only if the image will only be viewed on a color-managed system.
I know of no way to open an image in a "12-bit" mode. Can you clarify what you mean by that?
Regarding "8-bit"... You might choose to open a photo as 8 bit if you don't plan on doing a lot of image editing steps and/or your intended use is strictly for an 8 bit purpose such as saving a JPEG. Doing so simply uses fewer Computer Resources and will be faster.
There are also a fair number of features that will only work on 8 bit data - for example all the Filters in the Filter Gallery and a number of others. If you're using these effects you have to be working on 8 bit data.
People edited 8 bit images for years before the CS series made layers work with deep formats. People with Photoshop Elements still do have to use 8 bits/channel if they want to use layers.
I personally now always open raw files into 16 bits per channel, and convert only to 8 bits if I really need to. If your computer is up to the added stress of working on the larger datasets 16 bits/channel probably the best default to choose.