Where for a tube-newb to start?

Tand- I'm not sure, apart from old issues of the Tube Valley? magazine, maybe Glass Audio, mentioned above, that you'll find much in the way of scientific comparisons of tubes. There are tube data sheets for many tubes that are available for old tubes that compare specs. If you run a search for tube data sheets, you'll see what I mean, but other than electrical compatability, not sure those will tell you much about the sound.
What I was referring to was less of a commercial review, and more about user experience posting comparisons of different tubes in a given component (recognizing that different circuits may affect the outcome). I have posted such comments in various fora regarding comparisons of various rectifier tubes and my experience in rolling tubes in one of my phono stages. Garcia's reference to The Tube Store can also be supplemented by descriptions of various tubes on the Tubeworld website. I've bought a number of NOS tubes from him over the years. Good luck.

I've built kit amps and preamp, owned probably twenty different tube amps and probably even more tube preamps, and I have rolled many different tubes each with many manufacturers. Were I you, I would find out what tubes you have in there and go to audioasylum "tubes." and inquire about the best.

There are new tubes to be had, but in my experience those around the time of WW II were the best, but are almost unobtainable anymore. Forget trying to find Western Electric tubes unless you are very rich and in Japan.

Have fun!

One of the challenges is to find new tubes that have the character of the grail vintage tubes. There is a thread elsewhere here on Audiogon about the rectifier the OP wants info on- and various comparisons among users who have tried different new tubes. For that tube, I am using a Mullard first series fat base, which is one of the grail tubes, but even these aren't the kind of crazy money that some tubes fetch. (And I have a stash of other old rectifiers for this slot, all of which sound different in my particular piece of gear).
Ultimately, a lot of people use tubes like tone controls, to flavor the sound to their liking, within a given piece of gear, within the context of a particular system and listening bias. The whole notion of tube rolling is, in some ways, experimentation (subject to using the proper tube that is a correct equivalent). Unfortunately, as TBG said, some of the most desirable old tubes fetch big money.

The Cable Company has a pretty good selection of tubes. They'll give you recommendations for which tubes will work best for you.

Let me take a stab at providing some useful info. As a start, GZ34 and 5Ar4 are different designations for the same tube. It is a rectifier tube. The most popular old tube from the glory days were Millard GZ34 tube made at the Blackburn plant in England. Good ones are hard to find and expensive. A very good new production tube is the Gold Lion 5AR4. They go for about $40.

Is this the kind of info you want.