Uses for fondue broth

It's not a true Fondue but I've done something very similar by taking a white sauce base made with 50 / 50 wine and milk. You then melt in lots and lots of cheese and you get something very nice and similar to a fondue. You can pretty much use any reasonably melting cheese you like although a strong cheddar is very nice. For something really interesting add some Mozzerella and slowly melt it down and you get a wonderful stringy finish.

Assuming this is a meat fondue (AKA fondue bourguignonne), using oil instead of cheese:

There is no best or correct oil to use - each type of oil has its own characteristic flavour. However, a meat fondue generally involves heating the oil to 350-400° F (175-200° C), so you'll want to treat this more or less like deep-frying and use an oil with a relatively high smoke point.

That means, no unrefined olive oil, sesame oil or walnut oil, and be extra careful if you want to use butter (clarify it first). Canola, sunflower, peanut, grapeseed, etc. are all good choices, or any of the refined versions of olive/sesame/walnut with higher smoke points.

Personally I'd either use refined olive oil or a flavour-neutral oil like peanut or sunflower. Most of the time you don't want to be imparting any "foreign" flavours to meat, although I suppose you could go with refined sesame oil for a moderate Asian twist.