While there are a few things like EHT and round the LOP that can jump out and bite, this sort of set is largely no more electrically dangerous than a DAC90 or other radio with live chassis. All that you know about working with such radios is entirely valid for working with this TV so there's no need to worry on that account. All the caps will be totally discharged at the moment and will stay that way until you first connect power. For most of the caps the hazards are exactly the same as in a radio. The only extra thing to remember is that when you have EHT, the CRT can hold a charge for quite a long time after switching off. What's more, even if you discharge it, it can regain a charge. This is not directly dangerous, it's no more than a little sting, but if you jump and hit something then you might damage it or you.
The main extra hazard is a mechanical one. The CRT is a large amount of vacuum in a glass envelope. If you whack the faceplate or cone hard enough anyone standing in range will not be pleased about the trip to A&E. If you break the neck then all you will need is a another CRT. Please also try not to scratch the glass as this can give a localised stress point. Having told you how dangerous a CRT can be, in practice given just a touch of common sense there will be no problems at all. The glass is pretty tough and implosions are very rare.
The raster is simply the array of scanned lines on the screen, regardless of any picture information. I don't know the origin of the word.**
The Aurora will give you a test card simply by connecting it to a suitable power supply. This has been discussed elsewhere. Beware of the setting that lets it go into standby after a few minutes when no video input is connected. Several of us have been fooled by this. Read the manual for more info. Apart from the Aurora and power supply all you will need is a F to Belling & Lee adaptor or lead. If yours is anything but a very early Aurora it will also give audio tone in the absence of inputs. Once the set is giving test card and tone you can connect any video source to the Aurora. Such as a DVD player, VHS player, Freeview box, cable TV box etc.
To avoid damage to your lovely cabinet I make an unusual suggestion. That you jury rig a frame of wood, angle iron etc to hold the CRT, speaker and chassis securely. Effectively a skeleton cabinet that you can turn in any direction. I have never done this and I suggest it only in view of your lovely restoration.
I wouldn't bother to test the valves. Any problems will become evident as you run up the set.
Capacitor replacement is very much as in a radio except there are more of them. Any plastic dielectric types will do, 400V for most locations though there are a couple that I think need to be rather higher. Look at the markings since I don't think this is on the service data. As usual with a radio the cap on the mains should be removed altogether and replaced by an X rated type if you really want to retain a cap in that position.
**PS: I've just done a little online research and found that it's from a latin root about rakes and raking.
http://www.thefreedictionary.com/raster