It's doubtful that changing your init string is going to force the modem to connect at a faster speed since the modem already is connecting at what it feels is the best speed based on line conditions. That's what all of the screeching at the beginning is doing. It's possible with the init string to force the modem to only connect at certain speeds or to require it to connect at at least a minimum speed but it's doubtful that it is not already set to pick the fastest possible speed.
That said, before I could tell you where to change the string I would need to know what operating system you were using. Windows usually has a bunch of files with form mdmsomething.inf The mdmxxxx.inf files contain the string that windows uses to init the modem. Usually they start off with at&f which just sets the modem to the factory default then they tune a few parameters to make it work with windows. The problem is figuring out which one belongs to your modem.
Normally your modem manufacturer's website will provide a manual with a list of the AT commands which will also show the defaults. You can log onto your modem using hyperterm and give it an at&v command and it should show you how it is currently set up. You can compare to the defaults and see what has been changed. I would also need that info in order to tell you if there is anything that needs to be changed.
Ron