What size ratchets do I need to assemble some new equipment?
So it has a bolt that is 3 1/2" long with a 1/2" head, and a 1/2" nut... 

You're going to need a 1/2" socket and/or wrench, and/or a couple adjustable spanners. Looks like you're in the UK; so you probably use metric, So you'll need an 1/2" imperial socket and/or wrench, and/or a couple adjustable spanners.