You are running VMware Workstation on a Windows box that has its firewall set to drop ICMP echo packets. Fixing that depends on what version of windows you are running.

Do you want the guest machines to be able to access the Internet? If yes, then you want the NAT option. If no, then host-only should be sufficient to access them from the host. What about these options makes you think they will not work for you?

EDIT:

If you use the NAT mode, then you should be able to connect to the internet on the guest machines, providing you have them configured correctly (IPs in the correct range, correct gateway, etc.). Are you using a default installation of VMware workstation? If you configure the guests to be on the NAT network, and set them to DHCP, do they get addresses? If you can't use DHCP, you can use the VMware Virtual Network Editor to determine what IP range they should be on (check the NAT tab for the gateway IP address and the netmask, then assign them IPs in the same range--but not .1, as that is the host).

EDIT2:

To view the ip information on debian, run ifconfig -a.

--jed