To quote a friendly Irish man I once met,
"If you want to get there, I wouldn't be starting from here".
You made mistake #1 asking for an intelligent response from here.
You own an FZR250. This would be a fantastic bike to start racing with. If you are a racing newbie, forget all pretentions to 600 racing. Start with the 250 for at least one season and build from there. Ask Simon Volmer what he thinks of 250 4 cyl racing.
You can ride it in road trim because the rules preclude many mods.
Just spend some money getting new parts for it, get the engine fully serviced and get the suspension serviced and fixed up a bit (or buy a new shock absorber and fork internals), buy some good tyres and go racing.
Personally (only my opinion) I would not go for the Hyosung Cup. While it is great racing against similar bikes, the bikes are very difficult to really get anything out of, are not really designed for the task and are not actually all that cheap unless it is a bit shagged. If there was a Kawasaki Ninja version, then I would not hesitate in recommending going for that. If you have the money and don't want to race the FZR, go for a Ninja 250 and race in 250 Production. Best way to learn for not much money.
Join a coaching programme, go to ART days at AMCC, go check out the buckets and have a go there, but forget launching straight into big bike racing if you are as inexperienced as you suggest. That is simply a recipie for disaster and furthermore, racing a bike that is in road trim will just put you off as it simply won't work as well as other bikes that are out there and you will get discouraged, or hurt, or both. And $7k will not get you a 600 worth having if you have to buy other gear as well.
"Life is what happens to you while you're busy making other plans." John Ono Lennon.
"If you have never stared off into the distance then your life is a shame." Counting Crows
"The girls were in tight dresses, just like sweets in cellophane" Joe Jackson
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