Deepweed forces an awakened to astrally perceive, Shade works on mundanes, but forces even a mundane to astrally project.
You as a mundane suddenly projecting might be a really bad idea as it just opens you up to even more magic based attacks while your body back on the physical suddenly goes limp.
One on One with a mage you will face some difficulties, but that doesn't mean you can't win.
First thing is cheat.
Direct LOS at close to medium range between you and the mage is bad for you, unless you totally outclass them in the initiative department via souped up reflexes, because if the mage can see you he can blast/control/other you in a number of ways.
Use your smartgun link and guncam to shoot around corners.
Yes he can still drop an AOE type spell, but try to pick your terrain to limit these options.
Sitting next to something the mage won't want to wreck with an AOE will force them to more targeted options.
Again Smoke grenades can still help to some degree as can the fab based ones mentioned above.
There are a number of discussion threads about moving in stealth against astral observations, it may pay to look through some of them.
Snipe from a distance when possible, unless he has some binoculars handy he probably wont see you from a quarter klick out.
This may run into probs with the GM since he wont want the whole game devolving into SniperRun, but argue for its judicious usage given special circumstances and don't abuse it.
Use numbers to your advantage. There are a limited number of mages and other things magical in the world, use superior numbers to overwhelm/overload/distract them.
It may mean hiring street ganger muscle to storm the far fence thus drawing security's attention while you sneak in the side entrance or even just walk in the front door via a disguise. Or have a miniswarm of small drones harass the spirit while you go by.
Give the magical elements more than they can handle. Just be sure to have any forces keep well spread out so a single AOE spell or ability does not negate them in one blow.
Technology doesn't have drain, use that fact. They have fireballs, you have grenades. They have mind control, you have a plethora of drugs that can mess someone up.
A buddy with a chemistry degree, some dmso and some grenade making skills can give you some fun toys to add to your arsenal and you probably won't pass out from chucking just a few unless your aim is reaaalllly bad.

Drones are good but can be expensive. While they can not be directly mind controlled or manabombed, physical spells will chew them up but they are replacable whereas you are not.
Again, numbers play a part here.. keep harassing the mages with mooks/devices so they pile up the drain and can be easy pickings by the time you decide to step in to finish them.
Spirits will be a bit more work since drain is not an issue for them, but there are tons of energy based toys like tasers/S&S/lasers and such that can help disrupt a spirit just fine.
Again a pile of mooks/drones armed with these can disrupt low to moderate force entities or at least keep the bigger ones occupied while you go about your business.
You might complain about how using mooks/devices is not your style, but remember you against a spirit is the same as a lone soldier against a tank, it's two totally different categories of abilities clashing.
You have to be prepared to adapt your tactics accordingly.
There is no one 'magic bullet' (except for the one through the back of a mage's head) that can cure all your magical woes, otherwise everyone would be using it already.