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I know it's been 6 months, but hopefully this will help someone else.
Short Answer - Dail up should be fast enough for VoIP - There is almost no minimum speed requirement
Sound is a Wave that causes vibrations that we hear with our ears. humans speak in the range of around 100 ~ 4000 hz. music is in the range of 0~20000. so a conversation essentially have about 1/5 the data of a music file (this math is very rough and inaccurate, but it should illustrate the concept). you may remember from the days of 56k modems or even before when it would take like 20 min to send a 4 min mp3. so it seems like a conversation would barely make it over a 56k, this is especially true when you realize that phone convos require sending and receiving constantly, so your 56k is probably going to just about keep up with your phone call, maybe annoy you, but work
ANYTHING above that will be more than adequate, if you are looking at a 4-line or 8-line system now you have to consider DSL or cable
My DSL is so bad that I wouldn't dare try VoIP (I may be switching to cable soon). But I know several people who run VoIP off their DSL connections and say it's just fine.
Also, FWIW, a guy on About. com answering a question about VoIP bandwidth needs says, "The best bet is a DSL connection. As it goes beyond 90 kbps, you are good." That's a pretty low bar to clear (except for me and my DSL connection).
It may differ, but I when I have a WiFi connection, I use a VoIP app with my smartphone to avoid using up my voice minutes, and as long as I have around 2Mbps it works pretty well. Come to think of it, that's download speed, it still works ok if the upload speed is slower than that, at around 1Mbps. If I get less than that, people complain that my voice starts breaking up or there is lag. I'm not sure about other VoIP systems, but with what I use, you can change things like buffer settings and mic gain to balance voice quality with lag. It took me a while to find the proper balance, but now it seems to be as good as just using my cell phone as far as voice call quality is concerned.
Just as important as speed is latency. If there is a lot of latency, there is going to be lag. Nothing can be done about that. I find VoIP over 3G to be pretty much unusable, but I'm on Sprint, which is the slowest of the major providers.