If I understand you correctly, you’re looking to rip a board through its thickness, rather than its width, that’s commonly called resawing…..this:
So a handsaw is the kind of saw in the picture above, and the best kind of handsaw for re-sawing does depend a bit on the wood you’re resawing. Certainly, whatever kind of saw you get, you’ll want it to have its teeth filed to rip, rather than crosscut.
The length of the blade will depend on the size of board you want to process. For example, if you will be regularly resawing big boards…let’s say 4 inches thick and 22 inches across, then you’ll want to build or buy a roubo-style frame saw…here are a couple of examples:
Dieter Schmid sells a kit, I think Bad Axe does, too, or you can google around for DIY solutions, which are plentiful.
If you’re going to be mainly resawing boards that are somewhat smaller in size, say, 10 inches wide or less, then something around the size you mentioned, 24 inches, 22 inches, 26 inches etc will be fine.
The number of teeth: there’s some preference here, but I’d say for a Roubo frame saw, maybe 2-3 tpi, for a “normal” 22–26 inch handsaw, something in the 4-5 tpi range, maybe as many as 6 tpi, would be fine.
Paul has videos teaching proper resawing technique, so check those out asap.