So here's my list. This goes for every runner, whether they are hacker, mage, or samurai. Obviously, some types will have better than what you see here, but this is what I'd do as a minimum.
Commlink - All stats at 3+. Get at least one of the basic user program suites. You can default on things if you don't have the skill. You can't even attempt matrix actions without a program.
Identification and Licenses - At least two IDs, with licenses for all your non-forbidden gear. If you have a legit (non-criminal) SIN, then don't be afraid to use it if you don't have anything illegal on you, and you aren't doing anything wrong. The less you have to lie about, the less likely you are to screw up.
Ranged Weapon - Even if you are a bad-ass mage who can stunball entire rooms and not take any drain, or a hacker who can take down the ice on ZO without getting burned, some people react more to the visible deterrent of a guy with a gun. They don't know if you can use it or not, but a big gun always makes them think twice.
Melee weapon - whether it is a pair of hardliner gloves, or a katana, or a stun baton, having something to fall back on if people get in your face is a good thing, even if you have zero skills in that area.
Electronics - Tag eraser, glasses/goggles with an image link and any senses you might not have, white noise generator, subvocal mike, etc.
Survival gear - Gecko tape gloves, GPS, survival knife/kit, grapple gun with rope, and a medkit.
Restraints - Handcuffs, zipties, duct tape, what have you. If you can't figure out something to do with them, you're not trying hard enough.
Grenades - Flashbang or smoke for times when you need cover or a distraction. HE or Frag for tossing into tight spaces filled with bad guys. AP mines for traps. "Front towards Enemy", with a tripwire across a hallway...
Clothing - At least two or three outfits, all armored, naturally. I like to go with 'biz casual', 'social', and 'maximum firepower' layouts. Lined coat plus whatever armor gets you to your max but remains low key would be 'biz casual'. Something nicer/more expensive for 'social', ideally something that you could wear to Dante's and not get thrown out on your ear. And for those times when you are expecting heavy resistance, load up with the most armor you can handle, milspec if you got it, because when going into a 'maximum firepower' scenario, anyone that isn't looking heavily armored screams "mage", and you always geek that guy first.
Vehicles - Every runner should have some kind of vehicle. Even if it is just a crappy little Dodge Scoot scooter, you need a way to get from A to B if the rest of the team can't carry you. And taking a cab to a run location is just dumb. If it is a ride that can blend in with other vehicles on the road, even better.
Bolt hole - Get Runner's Companion and Safehouses. Make yourself the most comfortable 0-5 LP bolt hole you can. You'll thank me later when you need to hide out from the Oyabun's men because you pulled one too many jobs against his rengo.