Driving other of Costa Rica into another country

I read recently that requirements had changed, so suggest that you check at your nearest INS office.
Don't forget that even if you are driving your own vehicle you are 'expected' to have a return airline ticket back to your home country.
Personally, I would avoid the Paso Canoas border crossing. until the present situation has been addressed.

I have heard from others that driving into Panama or Nicaragua can be a pain, especially the first time and given my own experience visiting Panama I find some of the border people there to be real jerks which keep me from wanting to go there again. If I went I'd fly into Panama City but that's not cheap.

If you live closer to the Panama border than to Nicaragua then maybe it's worth it to try Panama but if I were you I'd take a bus or tour van or something down and then rent within Panama. That's what we did.