It all depends on the hardware that you are running on. You will need some ram for your host operating system, about 512MB for the virtualized server 2003 and about 256MB for the virtualized XP client. Those are minimums but are fine for testing domain connectivity.
If you are using VMWare Workstation you have a lot of options as far as virtual LANs, but even with the free player you can choose host only networking to keep them separate from other physical machines on your network.
As someone that has used both Virtual PC and VMWare products I can say that VMWare far outperforms Virtual PC, even when installing Microsoft's own operating systems. I think you are on the right path and will find that VMWare can do what you are looking for, and do it well.
Thats cool, but Microsoft releases those same images (prebuilt servers for 2003, SQL 2005 and so on) for VMWare to since it is the more popular platform. I don't remember Virtual PC having better networking, but they might have updated it some. I still don't see how they could have surpassed VMWare, but they might be close now. Plus the documentation and support for VMWare is very extensive. Sites, Forums and IRC channels dedicated to all the VMWare products. It just has a much larger userbase.
My last memory of Virtual PC was trying to setup an Exchange Server in a virtual Environment. Forrest Prep took 4 hours. We wiped it out, installed VMWare and recreated the virtual machines. This time Forrest Prep took 15 minutes.
Coming n/w point of view in you need to keep both the networks up and running so better use NAT for the Server OS and bridge the rest. If you have 2GB plus ram and a dual core processor with 2.6+ Clock speed I think you can a bit sluggishly but successfuly run both the OS at the same time.
and to the topic VMWare vs. VirtualPC -> VMWare actually provides many more flexibilities than that of VirtualPC with respect to device compatibilities and driver integration/interface between host and guest OS. Try installing Linux in VirtualPC it will get u the answer :)
how many of the VirtualPC users will know the fact that you just shared. I'm not against VirtualPC but it is quite evident that VMware scores lot better when you take the Guest/host interfacing or integration issues. Don't you feel this too ?