Hi!
I'll probably sound a bit dumb here, but take it as it seems.

I'm kinda experienced GM, but Shadowrun can be tough even for long-time plaers/GMs.
But, if you really look through the system, what you really have to do is to get confidence with the basic test structure and work with it during sessions.
I'd suggest avoding complex builds and don't exagerate with options.
Most of the time, complexity comes out (I'm not saying it's your fault, I'm just sayin' that it happens to everyone) from the fact that we read rulebooks without actually getti' the core assumptions.
SH 5ed evolves around a simple test structure (which you obviously know, but I report it to streghten the concept): SKILL + ATTRIBUTE [LIMIT] (threshold).
If you have doubts on how the game handles specific stuff, just stick with it. You have to make a "running contest"? Just Roll Running + Strength [Physical]. Who gets more hits wins. Don't care if the game states specific sub-rules about meters or something.
If that specific test is common, just scroll through the pages, find the rule in between sessions and that's it: you learned a rule.
The biggest mistake you can make is tryin' to master Shadowrun system. Just master the basics: everything evolves around that test construction, stick with that and let the game mechanics flow through the sessions.
If you're in the middle of a fire-fight, the worst thing you can do is quit and start lookin' and discussin' for rules: it's a lot worst than common-sense ruling. Try to find the soft-spot of the scene and work with that in advance.
Some advices:
EnemiesAre you gonna handle multiple enemies? Great: don't overprepare, just scratch down basic pools, like this (at least that's what I do):
Example of standard hit&die dude:
- physical attacks/defense: 8/9
- mental / social tests: 5
- damage: 8 + net hits.
- Absorb 8
- initiative 11 (usually do 4 + 6/9 depending on the character)
- Condition track: 8 (avoid multiple malus. You get -2 after 4 damage; die after another 4).
- Defense (+3 dice)
Don't mind if you don't have "body, agility or stuff". You have everything you need to know and you can fill a whole page with this mini shit with minimu variations, creating effective enemies for all tastes.
Better SheetsThere are sheets which are better than the standard ones, mostly because they've more space and are more clear to read. I attach an example.
Class ManagementHave your characters fill those extra sheets and note key stuff of their characters. A bunch of paper sheets work well too. Don't let them scroll through the book everytime: they can spend 10 minutes of their life to compile easy-to-access stuff for their own runners.
If you have a magician, just ask him to sign up her spells and effects (basic infos).
CheatsheetsAs suggested above, you can find many schemes on the web. Make a copy for yourself and one for the table, so that everyone gets in confidence with it and every player can help during tough scenes.
General managementElect one player to track down initiative and (possibly the same, but it's not needed) another to track down effects or something.
So that you can focus on "the black guy throws a bomb, it'll explode in 3 rounds (the elected players countdowns)"
Make it simple when it's obviousI see lots of players/GMs rolling for useless stuff.
Are you down, almost dead, disarmed and someone points a gun straight to your head? Boom. You're dead.

Ok, this is an extreme case, but that's how you should handle obvious scene: if you're crippled and someone at full health with a good athletic skill runs before you, you lose the contest. Period.
Just cut-off useless rolls and describe, so that the action flows and your players will take care of their choices and moves rather than "numbers".

Hope it helps.
My 2 nuyens.
Chhers