You need quite a deep box to mount a PID, at least 4 inches, so measure the thing up. I have mounted a DIN 1/16 PID in a 6"x6"x4" PVC junction box but it was a squash and I would recommend bigger. You need fat wires to carry 25A which take up space and don't like to bend.
Heat sink definitely, either mount it outside the box or ventilate the box with a fan and airholes.
Wood box a bit iffy, can't ground it and if it gets wet it will conduct electricity, plus it's flammable. Personally I don't see what's wrong with metal or PVC but doubtless it has been done. If you want something cheap and portable, check out some of the amazing and inspiring toolbox builds on this site.
Could do bus bars, could do terminal blocks like Kal's build, for me it's DIN bar terminals from Tier1 Automation.