" I wasn't sure if there was a specific reason to use fibre optic cables for the core switches so you've answered that for me."
Possibly just for the experience of using it. Remember, though, the principle reason (but not the only reasons) we use fiber is for longer distances.
"I'm assuming I will need to make up some crossover cables to connect up the switches?"
Possibly not, as @paul driver has already noted, some switches support auto MDI/MDI-X, i.e. you can use straight through or cross over cables. However, often this feature requires the switch's port to be in auto bandwidth/duplex mode to function.
"Is there a convention in how you connect up core switches regarding what interfaces to use?"
An "it depends" answers. Mentioned in my prior post, often edge type switches' uplink ports are "better" (usually for handling sustained loads) than other ports. (NB: one reason why there are "copper" SFPs. I.e. less expensive media for using a "better" port.) Distribution and/or core ports, might all be "equal" or not, often with those much depends on the particular "module" hosting the ports.
"I'm getting the feeling I may be overthinking it and they just need connecting in any way that means that if one switch went down, the other would still work. Am I on the right track?"
On the right track? I believe so. Of course, L2 and/or L3 need to be properly configured to use different paths.
