The Cisco router can probably perform the VPN functions you are looking for. The router could act as the concentrator. You could then connect to that router and establish the VPN. You would have a local LAN IP and communicate with your network securely. However, most people would probably tell you to let the router be a router and leave the VPN to a true VPN device.
PPTP or IPSEC in Windows 2003 are both fine for your needs. However, I have always prefered and had better luck using a dedicated hardware VPN concentrator. This allows for a network topology that may be more secure and also give you more remote control over your equipment on the LAN. A Cisco ASA would do the trick. You may try to get that in the IT budget. The ASAs are now using an SSL VPN with a different licensing model, so prepare accordingly. Some SOHO equipment may also be fine. Sonic Wall, Linksys, and others all have various VPN firewall/routers. You can even flash the firmware on a pair of residential routers to create a point to point VPN from your home to the office. It all depends on budget and performance requirements.
What are you currently using as a firewall at your office? That may have some built-in VPN functionality. You may also be able to authenticate the VPN off of your Active Directory depending on the device. If you have no device acting as an office firewall, please see the previous paragraph.
However, all that said, your problem is probably due to pass-through not occurring on your router. By default, the IPSEC and/or PPTP traffic will get dropped by your router without first telling the router what to do with that type of traffic in its config. It is similar to using port forwards for HTTP servers or Mail servers, the traffic required for the VPN connection must be forwarded.