Install a full time connection. This is the way to go if you have the need and the money. Install a router to your network and attach the router to a T1 line. A T1 line is a digital telephone line that is about 28 times faster than the fastest analog modem. It does not dial out to the ISP but stays connected at all times.
Response time is nearly instantaneous.
The down side is that it is expensive. The phone line costs several hundred dollars. The ISP will also charge several hundred dollars per month. If you have dozens of users to connect, you may want to consider this option.