You can use any Broadband signal, which includes DSL, but DSL is not preferred as it can still run very slowly. DSL, Fiber Optic, Cable Modem and Data T1s will all work without additional equipment. No point in moving backwards in technology, so I will not bore you with PRI T1 details.
If you have known ISP issues, there is not a lot you can do other than get a new vendor or host your servers in a data center where they will have multiple vendors and practically unlimited bandwidth. We usually set up a ping plotter to gauge the network, as latency and packet loss will be undetectable on a website, but a nuisance to VoIP traffic. Make sure all your equipment is hard wired in, no wi-fi and that all routers and modems are quality and configured properly. The only other interference I have seen as a direct result of an ISP is on the traffic itself. They tend to block or interfere with SIP traffic, so you may consider running the phones on IAX2 which will also work with the free Zoiper Classic soft phone.
Also, since you are doing all the heavy lifting when you are building up and tearing down the calls on your network, so make sure you have ample up and down load speeds. This will require some math on your part:
Bandwidth
On-site Agents: You will need 80 kilobits per active phone line you plan on using
Remote Agents*: You will need 80 kilobits per active phone line plus 100 kilobits per active agent
*agents from home, as opposed to in your building.