I have a few different lens cloths that I use. The ones I like most are the 50% Nylon, 50% Polyester. These were reccomended by Canon when I got my L series Lens and I use them on my riflescopes too. I think the type of cloth you use is going to change depending on the type of lens and brand of scope. Generally, lower end scopes don't have the real cool high tech coatings on them so they're a little easier to clean. The paper lens cleaning tissues would suit me just fine on them. On a coated lens, you couldn't pay me enough to put any tissue on it. Paper in general is abrasive.
As for the solvents. I've never seen any maker of lenses use harsh solvents. While several people here say they are recomended, I hadn't seen that and own some of the brands mentioned. I'll have to check that.
NEVER use stuff like window cleaner. I HAVE see where vendors state that window cleaner is harmful to some coatings. I steer clear of that. It also will never clean up. The cleaning solvents mentioned above are all an ultra pure version of the product. Alcohol needs to be very very pure to not leave a residue on the glass. I can buy into the saliva thing if you have a nice lens cloth since that will generaly come off completely. (lest your eating gummi fish or something).
I think I'd rather use a $15 5" square cloth than a shirt piece. My scopes and lenses generally cost enough that I'd opt for something I was sure had no foreign fiber in. While I'm sure some cotton shirts would be just fine, I'll get a lens cloth.
Head to a camera store and get something that they reccomend for high end glass. You'll be amazed how nice they clean and how fast. I'm just happier that the real nice lens cloths clean so fast I don't have to sit there rubbing forever. Less rubbing = less chance to drag dirt on the lens.
I usually clean my lenses dry. And, the best way to clean lenses is to not get them dirty. Get nice covers and use them. Most of the dirt I see comes from storage when not covered and I'm guilty of that myself on my cheapo 22's and such.