'Bead board' originally came in individual strips with tongue and groove joints on opposite edges (or sometimes double strips).
If you go to a real lumber yard you may be able to find it as single strips or double strips.
They have to be nailed up one by one through the tongue at an angle, just like laying a hardwood strip floor.
The plywood type is to try and save on installation cost, but it does make hiding joints harder.

get it at HD in the plywood section. 4x8 sheets.

Almost impossible to get a good butt joint---the 4' edges---with the 4' by 8' beadboard panels.

The better method it to install the single/double strips designed for linear and butt joint mating. Lumber yards usually have it.

Lowe's and HD websites blow goats. Lowes is utterly worthless, while HD is just mostly worthless...

I do buy from locally owned lumber yards when I can, I'm just trying to learn a little before I approach them.

Thanks for the help: this does help a LOT. The 36 inch stuff at HD is solid hardwood, available in cherry, oak, hickory or maple. Not sure if it's a sheet good or not, but would hate to have to deal with those short pieces.

Anyone know if the HD sheets are available in oak?

This whole project started as a means to disguise the long, narrow nature of the space, so I'd probably do the beadboard with 'beams' to hide the joints and create rectangles running opposite the long axis. 4x8 sheets would give me the most choice as to how large to do the rectangles, and would save some serious installation time.

The only 4'x8' beaded sheet goods I've ever seen at HD or Lowes is Plybead by Georgia Pacific. It's made from pine or something similar. It's meant for painted work. HD always keeps it in the plywood section not with the other panels.

I have seen 4'x8' oak veneer beaded plywood but only at lumber yards that cater to cabinet makers. You might have to ask a local cabinet maker where he gets his veneered plywoods.