office has 8 incoming POTS lines
You might want to look at the price for a telco T1 PRI instead, although keeping a POTS line for emergencies, alarms, etc. makes sense, too. And a 2 port T1 card, with one port connected to a channel bank, would probably let you support the existing analog phones and their wiring. Then you could migrate to SIP phones gradually, instead of ripping everything out.
Do I need to worry about the type of router used at the location?
Not if all the phone calls come in on analog lines.
The internet connection is not always reliable
If you add a DSL connection, then a device that can handle 2 WAN links would help, eg. pfSense appliance.