Combined router/modem for most small places (under 20 people) is best, and then a seperate switch for the LAN. Gigabit is only really needed if you have large files on a local server.
How is the DG834GT dying? There might be a problem that is nothing to do with the router, e.g. unreliable ADSL line, or people attacking the router, the mail server load might be flooding the device.
The things for wi-fi are probably wireless access points, or wireless bridges to link the buildings up.
Important if you normally have a specialist, then it is worth consulting them, as you may have things in place you are not aware of.