For new cigar experimenters, I would recommend hunting down some cigars from the following US cigar makers, in order to see what American tobaccos can taste like in a cigar. Avoid any that say, "imported." F.D. Grave used to make a truly wonderful burley cigar, wrapped in CT Shade, called "Judges Cave." Now, unfortunately, they've applied that name to a Dominican knock-off. All of these cigars are machine made, and most use short-filler. But some are 100% tobacco, rather than using homogenized sheet binders. Notice that I don't include most "drug store" brands, since these are generally awful.
National Cigar:
http://www.broadleafcigars.com/
F. D. Grave (Connecticut Valley Cigars):
http://www.fdgrave.com/
The Marsh Wheeling Deluxe Stogie uses Little Dutch, PA Red, and I think a Maryland. Their wrappers are CT Broadleaf, I think, for the "Dark." [Yes. I'm partial to the Deluxe Stogies!] Their Mountaineers are nice little smokes.
Nearly all of these cigars are made from what might be considered floor sweepings--cut filler, maybe homogenized sheet binders, etc., but they are authentic American smokes that are not in the Cuban tradition. Although I have made many cigars that would hold their own in the "premium" cigar arena, among those from the DR, Nicaragua, Honduras, etc., it's my American-style cigars that I enjoy the most.
Bob