I'm still learning but...I've read a little bit here on CC.
If you wanna go with plywood, I imagine a hardware type store like Lowe's or Home Depot would be able to pre-cut a piece of plywood to your desired diameter. They will probably ask you how thick. I'm not sure about this part. I'm not sure if it matters, except for the appearances.
As far as covering plywood, you know...I'm not sure. I'm sure you wouldn't want to put cake on a painted wood surface. And, I'm not sure if there is a particular way to cover plywood with fondant as I've never done that.
However, I have covered two cake bases recently. In my gallery you'll see a purple cake and a blue cake. They both are made of something called foam core board. You can get it in sheets at a craft store and sometimes at Walmart. There are different thicknesses. If your cake is going to be heavy, I guess you'd want a thicker board. I guess some craft stores will cut it for you...but I use an exacto knife to cut mine & it works okay. Just gotta be careful with the razor. Oh - foam core is pretty inexpensive.
Lots of folks cover their bases with regular fondant, marshmellow fondant, or I guess you could use rolled buttercream too. I do cookies mostly and love the combo recipe on CC that combines marshmellow fondant and rolled buttercream. It's pretty cheap to make.
Anyway, I'm not sure if there is something that is supposed to be brushed on the cake board or not before you apply your rolled out fondant. But, I just put it on there. I roll out as evenly as possible & then roll it up on my rolling pin & then un-roll over the board. I use a cake smoother to make sure it was smooth after applied, I brushed the excess powdered sugar off...then trimmed with my exacto knife. I made sure it hung over the top edge just a tiny bit. Then, I hot glued my ribbon around the base.
Well...that's what I did. Not sure if that's the exact way it should be done. Hopefully you'll get some more experienced people chiming in.