For the summary version, if you look on the main forums, the sticky thread of assembled SR lists, you will find one of magical traditions. It includes drain stats, as well as what spirits each tradition can summon (and how they associate those to the different categories of magic). Looking at it, you’ll find spirit types you are not familiar with from the core rules; you’ll also find those in Street Grimoire. You absolutely don’t need it to play with a mage, but it does offer a lot more – more traditions, more spells, more initiation info and meta-magic options, more magical nastiness of various sorts for you to torture your players with, etc.
Regarding getting SG, it is also available as a pdf for about half the price of the dead trees version. I’m using the pdf; it is a book where I think I’d prefer the physical version, but I’ve managed to wrestle out the information I need from the pdf.
As to your question about dealing with decking/astral stuff separate from other activities, well, maybe. They made a real effort in fifth edition to make deckers and technomancers come with the group, and to give them things to do in combat (reading through gear descriptions you’ll have noticed how many things have wireless bonuses? If you have your wireless on (to get those bonuses) there is the potential for a hacker of some description to breach your personal network and do things to your gun, your communications, your cyber eyes … Reviews of how useful that is seem to be mixed, but in general hackers won’t be sitting back in the apartment, doing their own thing, while the rest of the team is on a run because of the noise penalty for being far from your target (or so I’m told – no PC hacker in my game).
Now, if they are doing a bunch of virtual legwork ahead of time, of course that needs to get run separately, ditto for mages doing astral exploration. But for that matter: ditto for the face schmoozing a bunch of people without the distraction of bunch of twitchy and violent people tagging along. People may split up during legwork, but they should be back together for the main run, generally.
I wouldn’t worry too much about party composition or efficiency, so long as one PC won’t be eclipsing all of the others. SR tends to be so evocative that most people seem to have little trouble getting into the game and having fun for the sheer joy of being a troll levitating through the air while shooting lightning bolts, being the manic dwarf with all the big guns, etc. The challenge is in making events unfold in such a way that they can deal with the challenges with the abilities that they have (or can easily hire – NPC hackers show up with many groups, so that the GM can kind of hand-wave away much of the security issues. If someone wants to play a hacker of some sort then great, but it doesn’t always happen).