If you release and renew an IP before the DHCP lease expires, the DHCP server you connect to will almost certainly give you the exact same IP on the renew. That's why cable/dsl IPs change infrequently. To get a different IP each time you would need to change your MAC address each time...hrmm come to think of it if you did that many times in less than the lease time you could exhaust the DHCP server's supply of IPs and really make your provider mad.
Whatever your IP is won't make you secure or vulnerable...Patch everything, run a firewall/NAT router, and turn on your OS's built in firewall if you are worried about security. Get a linux/BSD router and set it up yourself to be sure that the rules really block what you are worried about if the above isn't enough. If you want a router that can do that use a linux/BSD box, or get the Linksys WRT54g and flash it with the sveasoft firmware and write your own iptables rules (linux).
Gaidin