New to tubes-how to handle? By the glass or base?

1st as carefully as possible. Try not to rock em back and forth. Just up and down if you can. If they are a 6sn7 or something with a base, sure, that will help. Most are all glass. I usally use a cloth. Also, clean the pins and sockets with a good contact cleaner like Kontak.

Good luck! The less handling the better. Don't turn them on and off to much. Ie...if you are listening for a bit, then going away for a few hours, then listening again, I'd leave them on. I usually leave everything powered up all weekend, then on and off during the week...this is subject to differing opinions...

I agree with Jfrech. The only thing I do differently - and admittedly I'm a little AR about this - I don surgical gloves when handling the tubes. This sounds a bit extreme, but everyone's hands, no matter how clean, can leave behind an oily residue that adversely impacts the performance of the tubes. It gives you much greater control and reduces the likelihood that you might bend or break one of the pins. Or that the tube might slip and fall onto the floor.

Happy listening!

One thing that is important is not to handle the tube while it is hot- this is when they are the most fragile. The longer you let them cool, the better. It is considered proper to handle them by the base whenever possible. As for as rocking goes, and i'm sure this is what Jfrch means, is that you don't want to rock them so much as to tork the tube and cause stress to it, but you should gently wiggle it as you lift. The idea is to get it out (and in) with as little stress to the tube as possible. Nothing at all wrong with rubber gloves, fingerprints can and do get etched on, especailly hot or warm tubes. A rag or napkin is good, and you can wipe the tube clean at the same time. Be weary of contact cleaners, while it is important for clean sockets, be sure to let them dry so you don't get arching, that is very bad, which is why cleaning is so important, besides sound quality.
Tubes wear because of heat- the delicate metel parts can only last so long (years) in a heated state before the metallurgy wears down. Heating and cooling actually is harder on the tube, so there is a point where one is more harmful than the other.
When you store them, be sure not to put them in a box or such where they can bang against each other or other things. I have lost some good tubes from this. It doesn't take much to break them, evan if you are gentle. The induvidual boxes are fine, and if you don't have them a napkin with a rubber band will do the trick.