Going outbound from behind the router shouldn't be a problem. Going from "outside" the router in will be a pain, but can be done.
You have a couple options. You can set the outside ports for the applications to point inside to specific machines (one port, like FTP, points to one machine), or you can put ONE machine in the router's DMZ and it'll be accessable from the outside (everything, all ports).
The problem is that whatever you open up for the outside network, also allows anyone from the Internet to get to it as well. Everything on the outside (the other network, the Internet) is treated the same. If you open FTP for the other network, then the Internet population can see it too. There's no getting around it with the consumer-grade router/firewall/switch boxes (none that I know of).
Since the other network is exposed to the Internet all the time as well, connecting the two behind the firewall would be a big security risk. Once one machine is compromised, it's possible for the attacker to leapfrog from that machine to the others (depends on the attack).
Good Luck
Scott