Hello,
welcome to the show
My own opinions regarding your questions:
- T-Rex 500 is good choice.
- Buy 2.4 GHz 7 channel Futaba.
- If you hate reading manuals above everything else, get Futaba 401 gyro. Otherwise avoid it.
As already indicated, this (my) post is full of opinions... The less conclusive a question is, the longer it usually gets discussed. Well, this is -my- answer.
Many beginners I know start on T-Rex 450. 500 size is easier and in the end more capable, but considerably more expensive. For that reason I fly 450 (another opinion...)
Be aware that most likely you'll spend half of the money on the batteries and chargers.
Generally, you can (means, I do) manage with one expensive balancing charger (Bantam BC 6-10 € 160) - if you pay attention - and use several cheaper chargers (i.e. Bantam LP 6, ~€52) to do most of the work. Prices are from verticalhobby in Espoo.
And, if you're serious about the hobby, get a decent sim (Phoenix RC) together with the radio. With regard to "serious about the hobby", 100 hours will get you somewhere, but it's not excessive.
To put that into context, 100 hours are two-and-a-half weeks working full-time. Think that through, before spending a lot of money. A coax heli might give you the wrong impression. It's more of an RC car than a heli.
The rudder (left stick left/right) is all wrong in FMS. I learned on FMS, but some people have had problems with it (Well, it's not "all wrong" but it models gyro rate mode. No beginner would want to use that).
And finally, the "3dee" in FMS is not aggressive. It's a joke, and if one day you've got the 500 under control you'll laugh about its "aggressive" character. Jeez, it can barely lift its own weight
Needless to say, for a beginner one can easily tune it down a bit and reduce the maximum power.
PS: According to Maikko's experience (check "Torppaukset") I suspect that the belt-driven version is the better choice.