To kill two birds, the alt-presets supposedly do more than what you can do with command line stuff. They supposedly modify LAME internals otherwise unmodifiable. Most folks seem to suggest using them.

The minimum bitrate is the lowest bitrate that lame will use in a vbr file. If you set it lower, a very easily compressible block will use it. If not, it won't. There shouldn't be a problem setting the minimum lower. But if you hear artifacts, try setting it higher, as it's possible that lame got faked out by a block and used less data than it really needed. This shouldn't happen and would be a bug, but the minimum would hide it.