Hey Andy, you can always look to an Epiphone Casino or a Dot, I have had a Casino for years and it does well for dirty old rock and roll as well as cleaning up nicely for jazz sounds. If you want to specialise it for Jazz, then throw on some flat wounds and knock back the tone. They are really versatile.
The ibbys are great as well, I’ve played a couple and they have a good feel to them but as Simon says, you need to aim mid range model or top end.
eastman are also nice, but that is another step up in cost although they are lovely guitars.