For an internal cluster (db server, web servers etc..), is it good idea to use IPv6, which is faster and more secure? And make use of IPv4 just for the internet connection.
Is it good idea? (sorry for the newbe'ish question).
That depends - When people say "faster and more secure" to me, that sounds more like marketing blurb than a proper technical judgement, but if you can point to specific reasons why IPv6 will be "faster and more secure" for your specific scenario and you can be sure that these benefits will outweigh any cost of making the change then by all means do it. In other words, does IPv6 fix a problem you actually have right now?
I have to say that personally I wouldn't have part of my internal network using IPv4 and part using IPv6 so for me the question would actually be "Should my whole internal network be using IPv6". Any speed and security gains you might get from making part of the network IPv6 will be negated by the support costs of a mixed environment and IIRC the need for a IPv6 --> IPv4 gateway in a mixed network will tend to negate any technical benefits.
IPv6 is more secure but for internal use I don't see that extra security as particularly worth it as I have lots of other security measures in place that I think are stronger (hardware firewalls, IPSec/IPTables etc.). Personally I use v4 internally and currently dual-advertise (4 & 6) our external services.
Oh and this is a good question by the way :)