It will be a 1/4 wave vertical for 80 meters.

I have a question regarding the radials I'll be putting out. I
was planning on using solid #12 copper, and was going to lay out about
500 feet total of radial.

Am I better off to use fewer and longer, or shorter and more?
I'm inclined toward 10 50 foot radials. I have heard opposing views on
the "proper" length of radials. (I'm assuming that longer and more
would be much better, but I have some practical considerations here)

If you only use that much wire, go with shorter. However, you will want
to put down quite a but more wire than that to get good performance.

The rule of thumb I use is a minimum of 50 radials, with length
at least the length of the vertical.

I currently have up a similar antenna- a full size wire 80m vertical
hanging from a tree fed in parallel with a 160m inverted L. So far I
have about 65 radials ranging from 50' to 100' in length. The antenna
works great on 80, even for far DX such as 9M6. On 160 it is fairly
good, but I feel I still need more radials.

Torsten
N4OGW