Welcome from Columbus.

When cutting cigars i had the same problem at first. You should not try to cut the full width of the cigar in my opinion, but rather cut the cap smaller than the diameter of the cigar to help maintain the wrapper. I don't like punch's, the tar tends to build around the small hole and cause a bitter taste.

Some of my favorites you may like include the Oliva serie g camaroon and the cao gold maduro. both smooth medium to light smokes.

also try eating before a strong cigar, it may help with the vomit situation.