OSPFv3

If you control OSPFv2 (IPv4 OSPF) wou wont have any problems here. There are, however, a few differences in the configuration. First one - it's configured on the INTERFACE LEVEL, and the Area is also defined there, so there is no need to add the "network" commands within the Router configuration:
(config-if)#ipv6 ospf 1 area 0

!!!Dont forget to define the router-id, because if there are no IPv4 addresses on the router - it cannot pick one! So - FIRST define the RID, and THEN configure OSPF, to avoid restarting the OSPF process later.

LSA Changes: Even though most LSA definitions stay the same, there are a few changes in OSPFv3:

OSPFv3 OSPFv2
0x2001 Router LSA 1 Router LSA
0x2002 Network LSA 2 Network LSA
0x2003 Inter-area Prefix LSA 3 Network Summary LSA
0x2004 Inter-area Router LSA 4 ASBR Summary LSA
0x4005 AS-External LSA 5 AS-External LSA
0x2006 Group Membership LSA 6 Group Membership LSA
0x2007 Type-7 LSA 7 NSSA External LSA
0x0008 Link LSA
0x2009 Intra-area Prefix LSA

*If you want an area not to receive LSA4 and LSA5, configure it as stub:
(config-rtr)#area 12 stub <- ADDS A DEFAULT ROUTE TO ISOLATED ROUTER (the router that only has stub area)
Default Route added: OI  ::/0 [110/2] via FE80::2, FastEthernet0/0 <- INSTEAD OF ALL EXTERNAL ROUTES

If you want the router to maintain IO INTRA AREA routes only, configure it as NSSA "stub no-summary"

If you want not to propagate EXTERNAL routes- configure an area as NSSA (routes redistributed into NSSA area will appear marked with "ON2"). You can add "default-information-originate" to inject the default route into nssa area. Add "always" to this command if you want to inject the default route, and the local router doesnt have one.

To change the METRIC/COST you can do two things. Either change the DEFAULT COST under OSPF process:
(config-rtr)#auto-cost reference-bandwidth 10000

Or use the "ipv6 ospf cost" command under EACH INTERFACE.