Okay,
Perhaps I can clear this up. I have a .22+ that I've rebuilt extensively. Also, I have quite a bit of experience working on electronics. Especially tube guitar amps. I'm not tooting my horn, I just want to give you some definitive answers that you can trust.
LHanson is right about this amp not having a Class A power section. Mine certainly does not. If yours is really old and has a vastly different design than I will stand corrected. But, I'm sticking to this theory for now.
Your preamp is, in a way, Class A. However, that is generally assumed since all preamps are this way(Generally Speaking). What I mean by "In a way" is that by definition, the single ended nature of your preamp circiut makes it Class A.
The term "Self Biasing" is a wierd one. I'm not sure what this means but I've never seen such a thing in any of the amps I've ever worked on from Fender, Marshall, Mesa, Rivera and so on. Here is the real answer to your question:
No (LHanson is right about this). Just put in new tubes. Evrything will be fine. FYI, Your Preamp tubes are "Cathode Biased". Because of this, you can't adjust the bias without changing some resistors.
Also FYI: Your power section, which is Class A/B, is what is called "Fixed Biased". This is done by aplying negative voltage to the Grid and is usually adjustable. Mesa doesn't let you adjust it because they want you to use tubes that are within a certain spec. These tubes are available from Mesa and Eurotubes to name a few. For best results you need to use these tubes. They are NOT "Self Biasing", whatever that is.
As far as the speaker goes, I vote for a Vintage 30 from Celestion.
The .22+ is a bad *** little amp. Congrats!