Okay, so gear. I'm going to hit the highlights: Commlink, armor, and weapons; you seem to have widgets figured out and those are kind of subjective anyways.
Armor: You should own a suit of Form-Fitting Body Armor (Arsenal) to wear under your other armor. It is really good, because it is 6/2 armor that counts as 3/1 for encumbrance, stacks with everything else, and is legal and discrete.
On top of that, you want another 5/7 of armor. I'm going to recommend a Synergist Business Line suit jacket and skirt (4/3, and also provides -2 concealability to things you hide in it, by which I mean guns), and SecureTech PPP Systems vitals protector, forearm guards, and shin guards (also worn under your clothes), but you can find other ways to get the same armor depending on your taste in fashion and how much time you want to spend playing Pretty Princess Shadowrun Dressup. The end goal should be to wear armor that is fashionable-looking but also bulletproof. You can tack on armor mods like Nonconductivity and Chemical Protection if you have the spare nuyen.
Weapons:
Ruger Thunderbolt (750) with Internal Smartgun System Option (400), Personalized Grip (100), Chameleon Coating (1000), Underbarrel Weight (25), Powered Folding Stock (100) [load with Ex-Ex]
Yamaha Pulsar (150), Underbarrel Weight (25)
Morissey Elan (450) with Internal Smartgun System (450), Underbarrel Weight (25), Chameleon Coating (1000)
Yamaha Sakura Fubuki (2000) with External Smartgun System (400), Chameleon Coating (1000), Silencer (200) [load with Stick-n-Shock]
You don't need to start with all of these guns, but I recommend starting with the Ruger and the Yamaha Pulsar at least. The Ruger does solid lethal damage and is good for killing people and destroying drones. The Yamaha Pulsar is legal and a good taser. The Morissey Elan is really easy to hide and can get past MAD scanners. The YSF is easier to hide than the ruger, just as good when using Stick-n-Shock, and holds more ammo; it isn't as good for doing lethal damage, though.
Commlinks: Here's a good package that will get you basic matrix functionality at a reasonable price.
MetaLink with Vector Xim (300)
Runs in Public Mode broadcasting fake SIN, not used for shadowrunning
Sony Emperor (700) with Novatech Navi (1500)
Upgrade Response to 4 (2000)
System 4, Response 4, Firewall 3, Signal 3
Optimization: Browse (500)
Powersuite (Analyze 3, Browse 4, Command 2, Edit 4, Purge 4, Scan 2) (1240)
Encrypt 1 (100)
Agent, Pilot Rating 4 (10500)
Runs in Hidden Mode, used for shadowrunning persona and running gear. The agent normally runs Analyze
to watch for any intrusion and will sound an alert if it finds anyone.
You can also pick up nifty stuff like gait analysis software, facial recognition software, etc. If your GM allows empathy software, you should start with Rating 5 Empathy software with the Optimization 2 program option for +5 to all social skills, and go hunting for Rating 6 Optimization 3 empathy software ASAP. It's commonly houseruled away, because it's super cheap and there's no reason for everyone not to run it, so check with your GM.
If you have BP left over, I would try to get your rating 2-3 skills up to 4. If not, I would shuffle them so they start at either 1 or 4 and then buy stuff with karma. The reason for this is because of the way karma advancement works: rating 1 or 2 is 4 BP or 4 karma. Rating 3 is 4 BP or 6 karma. Rating 4 is 4 BP or 8 karma. So rather than start with, say, 3 skills at 3 and buy them all to 4 for 24 karma, you can start with 2 skills at 4 and one skill at 1, and buy it up to 4 for only 18 karma.
The Infiltration skill and the Palming skill are things you might find you want after gameplay starts, depending on your group and GM's style. You can probably afford to buy them with Karma, though. On which note, you should spend your first chunks of karma buying the specializations Perception (Visual) and Pistols (Semi-Automatics). If you do get Infiltration, I recommend the Urban specialization.