First up, based on your initial description, I would recommend starting out simple and follow the Missions guidelines to begin with. For one, it gives your players some initial restrictions to reside in and gives you a chance to ease yourself into the game system. That first mission, Chasin' the Wind, is a decent introduction to Fifth edition (and Shadowrun as a whole), because it was the first mission written after the new rules were made available. It is also a decent introduction into the setting of Shadowrun, throwing a variety of circumstances at the group without being too overwhelming.
Now, to answer your specific questions:
1. The Missions Organized Play guidelines are a common "rule of thumb" for a lot of people. They limit several character options that would normally require a lot of GM interaction to make them work the way they should. For a home campaign, a lot of them are fine, but it gives you a good idea of things to watch out for at the very least.
2. No particularly easy way to read stat blocks. Some missions tend to write the skills as Dice Pools instead of Skill Ratings, which is something to watch out for. On the one hand, it makes it easy to just grab the number and go, but on the other hand, it can be harder to figure out situational modifiers or if they are writing out the values correctly. Not to mention when the default attribute is different than a particular situation demands. Reaction + Pistols to quick-draw, for instance...
3. For my game, I usually use theater of the mind. Sometimes I draw out a quick sketch of the battle-field to give people an idea of layout. Usually, distances are too big to be good for using a battlemap. At least in my experience.
3a. If, however, you like using battlemaps and minis, there is actually a kickstarter going right now for some guys that do flat-plastic high quality printed images. Check out the kickstarter page
HERE. One of the sets you can get is a Cyberpunk theme, and I'm pretty sure it is specifically for Shadowrun, since it has orks and trolls...
4. That Chasin' the Wind should have some information on various Legwork that the characters could do. And a lot of it is stuff where asking around with your contacts is an easy way to get things done. In my experience, that's usually the best way to get players to talk to contacts. Just suggest that they ask around about something. In the end, it is important to remember that most people don't do everything on their own, they ask for help and interact with others, which is exactly what contacts are for.
5. If your players want more options for character customization, go with Run Faster. If they want more weapons/armor and options for combat, Run & Gun. Past that, it is really based on what character types you end up with. Street Grimoire for Magic-types, Data Trails for Matrix-heavy. Chrome Flesh for More Augmentations, and Rigger 5.0 for vehicle customization.