Install DNS on the 2008 server and add it into the zone as a secondary server, then make it SOA for the zone, then take out the old (after telling DHCP to point the clients to the new server)
For DHCP just create a new one with the same scopes and settings etc, set conflict detection to 1 or 2 and then just de-authorise the old one.
Unless you really want to preserve the DB, you can take it over but to be honest on a small implementation then its often not worth the time when it can just re-create itself.
On a big bloke though you'll want to take the DB over. Done it a few times on NT 4 to 2k upgrades but never from 2k3 to 2k8 thus far.