They should be able to give you the best possible string to use. Also, most new software automatically detects the type of modem you have and uses its own initialization string. Telephone line technology and quality are important factors here. Modems rated at 28.8 Kbps were the first ones to retrain themselves while connected. This is especially true of 33.6 Kbps or faster modems.
Cordless phones can cause slow modem speeds by introducing interference on the phone.
If you still have problems, try temporarily disconnecting ALL telephone devices other than the modem from the phone line. This includes phones, faxes, modems other than the one you are testing, splitters, wireless boosters, etc. After checking the phone lines within your building and the items suggested above, call your local telephone company and ask them to check the quality of your phone line. The Internet's a big web of networks. If one of the networks in between you and the place you're downloading from is really busy, then you're going to see sluggish performance.