You won't need a crossover cable unless you have either very old routers, or very expensive routers that only do routing. Basically if you have 2 home routers which I suspect you have, they are not just routers, they are routers with integrated 4 or 5 port switches, so you have your router which is the wan port on the unit itself (external interface) and a port hooked up directly to the switch inside the unit itself that you cant see (usually directly soldered). Because it is then switch to switch, you don't need a crossover cable because they auto detect which wires are transmitting and receiving data.
As for the DHCP, it really depends on your IP range setup for your network and how you want to deal with that.
There's a few scenarios here:
If both routers are ADSL, both routers management interfaces are going to be on the same network as they'll be connected via the integrated switch part of the router rather than the other side of the WAN port. This would mean either router could give out DHCP, providing you had the correct settings for the default gateway and don't just leave it as default on the one that isn't plugged into the phone line otherwise no-one will be going anywhere. The problem with that is you have people you don't want to get on the internet. Assuming neither router has functionality to block users from getting on the net, it could be difficult getting around that.
If you had a cable router and an ADSL router it'd be ok, as you can just hang the ADSL router off the WAN port on the cable router, and run DHCP on both - leaving out a default gateway on the cable router so no-one connected to that can get on the net, and connecting people you do want to get on the net to the ADSL router, but I doubt you have that setup...
Soooo, in the case of 2 ADSL routers... Connect them together via the integrated switches, set static IP's on the machines you don't want to get on the net leaving out the default gateway, set up DHCP on either as you would normally and that'll work nicely.