You say "unlimited budget" and then you go on to say you have a ceiling of 500 or so for price total. Really, 500 isn't much at all. If you wanted, you can use one plane transmitter if you're willing to. Then I'd suggest either going electric (with a bit better one so it doesn't get tossed in the wind) like the trex 450 mentioned above, or going for a 30 size nitro (to keep cost of electronics down because they don't have to be quite as good in the 30 as the 50) and go with a century hawk or hirobo shuttle.

A lot of the helicopters on the market use what's called CCPM and in order to use one of your existing transmitters with those models it will need to work with CCPM. The Century Hawk doesn't use CCPM and is a very nice heli, so even if your transmitter doesn't support it then that would be a great heli to start with.