Wow....loaded questions man. I'm not quite that technically minded...I'll can say that you have to know your equipment. I experiemented with various levels and effects to get that crisp sound. If you have a good mic, and your levels are correct, you shoud not distort...my system also has a built in compressor which aids in this (its a Sampson Expedition, and basically what you see in the vid is the system...two speakers, with a built in mixer on one of them) It did not distort once while I performed. And I think that just comes from knowing yer equipment.
I've never been a big fan of the Shure mics...I'm assuming you're referring to the choir mics that hang overhead. They tend to pick up a lot of ambient sound unless you really know what yer doing. Tho take that for what it is worth...I've used them only in choir performance and have been less than thrilled...for a solo show, who knows? Unless they are set up correctly, be prepared for lots of feedback.
As far as lisping and popping, a wind filter is the best you can do I think, especially with a headset. If you're using a standard mic, you could always place a wondscreen, but it would block your face....perhaps someone else can be of more assistance with that facet of your question. I've leanred how to not do that (popping and lisping) just from practicing.
The mic I used for this show was an "audio-technica" Pro 8HEx (MSRP $79.99) I really enjoyed it. It has a nice crisp sound and didn't give me any of the problems you seemed to be having.
I hope this helps....I'm sure there are more technically minded ppl here who could be of better help to ya
Jason