Would you also recommend some different drinks for different Tats?
No. Some folks enjoy smokes with beer, wine, or fine spirits. I am a fan of all of the above. I believe that good wine, beer, and single malt scotches each have their respective places. I prefer to enjoy them alone and without complicating the palate with a fine cigar. The flavors in each are very pronounced and should be experienced without dilution or confusion, especially if you are spending good coin on the drink.
Coffee, on the other hand, is a flavor that is often noted in some of the best smokes. Drinking a good cup seems to enhance or bring out the flavors or even compliment the cigar. (Unless the cigar is an acid, in which case, you should try drinking drain cleaner while you smoke it.) I have found this to be the case not only with Tats, but with Olivas, Fuentes, Pardons, HCs, etc.