Ok, this is where things get a bit tricky, as both magic AND the matrix are CORE to the setting and feel of shadowrun. But, they can easily over whelm a new group of players (let alone a new GM!).
I would suggest that you talk to your players, and find out if they have any excitement for either before you cut anything. Obviously, you don't want to cut something your players are interested in

But assuming you have done that and decided to cut:
The matrix:
If you are looking to get rid of technos and decking, while still keeping the technological feel of SR, the easiest way is probably an NPC decker and "Handwavium". Have the NPC deal with the matrix issues and "hand wave" the results as needed to advance the plot or add complications. Just DO NOT let the npc over shine the players in any way. The npc should be a "follow the leader" type, and there to assist the players, not take away their fun.
This allows you to play up the matrix side of SR in a more RP fashion to introduce the players to it and its interaction with the world. As you get more comfortable with the matrix rules, you can slowly include more and more in for your players to experience; with out a "sink or swim" feel to it.
Magic:
Keeping the same feel of SR and magic with out actually smacking your players with it is both hard, and easy. On the Easy side, magic use is actually super rare! Only about 2% of the world population is awakened, even less have the training to actually DO something with it. But those few that can actually DO something? Yea, they CAN DO SOMETHING!!
So, the first option is the same as for decking, just for magic, and for all the same reasons.
The next option, is to have magic around them, but they themselves never actually, directly confront it. So while they may see spirits manifest, or spell effects, they will never actuall fight a spirit, or be hit by a spell.
By canon, this IS possible (however, highly unlikely), given how rare magic is. But this also places a challenge on you, as higher end facilities (especially AA+) almost always have magical protections of some sort.... but then again, this hives you the option of slowly introducing magical threats at a pace you feel your players can adjust to.