A PCR hood is a clean bench, which means it blows HEPA filtered air either towards the user or down and towards the user. With a PCR hood there is no personal protection, but there is product protection -- you are protecting your PCR setup from contamination.

A fume hood draws lab air into the hood and out of the building. This provides good personal protection, but does not protect your experiment from contaminants in the room. If you use a fume hood for PCR setup you might contaminate your reaction with previous PCR products or other templates.

A biosafety cabinet (BSC) blows down HEPA filtered air and has a slight draw in, but not over the working space. A BSC protects both the person and the product (although it won't protect you from solvents unless it is specifically designed to exhaust via hard ducting). A BSC would also be a good place to setup PCR; although quite a bit more expensive than a PCR hood.

You do not want to be setting up PCR in a fume hood. It offers no protection to you or to your reagents.

Unless you are working with samples where contamination with human DNA (e.g. your DNA) is a concern, you don't need to bother with a PCR hood either.

PCR is a standard, set it up on your bench, sort of protocol.

For each PCR step, there is an adequate cabinet, see attached picture.