Maybe a stupid question, but what sort of lampholder do I need to buy for this light which takes the cheaper halogen 250w lights?

The A1/259 250W/24V lamps need a GX5.3 holder.
There are a few variants of it though, so you need to see what yours looks like. The two main ones are either a rectangulat one about 1" x 0.5" or a circular one about 0.5" diameter.

They are only a few quid, try to go for a branded one though.

Jim

Geni tend to use this sort of thing but with white wires, it can be replaced with the ones Jim says.

One other thing to watch for is the mounting holes need to match up if you don't want to start drilling.

Jim

Good point. I will take the old one with me when I buy the replacement!