Line noise and signal degradation is common when plugging additional telephone devices into the same wiring set.

As far as ping is concerned, that could just be normal latency fluctuation (normal with modems), or it could be a symptom of the line nose.

I recommend that you get broadband (DSL, cable-modem, 802.11 wireless, ISDN) service if it is available. This will solve both problems extremely well.

Note that satellite service (DirectPC, Starband), although it is broadband and will solve the download speed problems, will not solve the ping problem. Those services have lousy pings, sometimes worse than modem.

If you do not have broadband service available, I recommend getting a separate telephone line just for the data connection. Plug only one or two computers into the data jack. This will make things work as they were intended, but it isn't as nice as broadband.