I like the shiny Fizik tape for all three of the reasons you list in your criteria. It cleans really easy, provides good grip and it lasted me a full season and I only removed it to overhaul the bike.
Fizik fuzzy, not so much.
Ah, I wanted to like the Fizik tape but found the padding to be less that desireable (compared to cork-ish types). I also found it not as grippy as cork-types.
And the Lizard SKins tape workes great for a short while - indeed, gets very grippy - but that out "grippy" layer will wear through to the white foam underneath in about a season. If you change tape regularly it's not a problem, but it does cost more than others.
For me, for now, it's Planet Bike or the Bontrager stuff listed below. Sometimes I'll go with a roll of cloth tape over the cork-ish stuff.
Some years ago I had a couple rolls of "RooX" I believe, incredibly grippy stuff. Wish I could find that again.
This very much seems to be a "YMMV" topic. Bar tape isn't terribly expensive, you can experiment with a few different types.
I am a huge fan of this stuff. It's labeled under several brands. It's grippy, padded, nice colors and holds up very well. Great grip when wet too.
I was a die hard Cinelli Cork guy (belies the roadie back ground) but last season, at the suggestion of a team mate, I started using Lizard Skins DSP bar tape in the 2.5mm thickness. It cleans off better than the Cinelli (in fact you can remove it to wash it and then put it back on, is super durable, comfortable, and gets grippier when wet.