The answer depends to a degree whether you are JAA or FAA.
I believe a jet requires a type rating under either regime, though under FAA a TR is mandatory only if above 12500lb.
A TR is not a big deal; it's just a load of training on type which you obviously need anyway. I am informed (not having bought a jet lately
) that while one can fly a jet on a PPL (sort of workable in the USA where you can go VFR below 18,000ft) it's hard to find anybody who will teach you the TR if you don't have an IR and something like 500-800hrs TT, but you have that already. Last time I asked (CJ1) it was PPL/IR and 800hrs but that was N-reg.
Insurance requirement can be a big issue; in fact the great majority of light jets are not flown by the owner.
The U.S. "Flying" magazine is a good source of info on upmarket flying like this, and IFR matters generally.