If you really don't like modem connections & don't want anything to do with them, I think you can filter them out. I don't have LW on this comp as my other one is in service at present. I can't remember where to find that option. Probably in the Tools>Options>Downlds part.

Why you should get stuck with modem everytime you browse or select to downld, I'm not sure. I'd like to say it's just poor luck, but since it happens so often for you. I haven't experienced this & I tend to browse a lot. When I started with LW (v.2), you could separate sources. But you can't anymore. I can only suggest to search more, browse & browse those browse results that have multiple results. Then you might find better/faster sources. And also downld from multiple sources.

Keep in mind that there's also some other clients out there such as Shareaza (RAZA) which have a tendency to only offer 0.1 to 3 KB/s. This is due to them using their uplds for another network where they can only downld as fast as they can upld.