RAW you can't initiate at char gen. Away from book, but the char gen section specifically says what you can spend Karma on. Off the top of my head, Attributes, Skills, Nuyen, and Qualities was it. No spells, initiation, or bonding with Foci.
Firing Squad adds Martial Arts to the list of things you can spend Karma on at Char gen.
Re: Multiple combat skills. Max out Agility. Get a +4 to Agility however you're planning on doing that. (Drugs, Magic, 'ware, whatever). Pick one Combat Skill and max it out at 6, pick up a Specialization with Karma. Buy a skill of 1 and a Specialization with Karma on the other combat skill. 10 Agility plus 1 Skill and 2 from Specialization gets you 13 dice which is good 'nuff for a back up.
You're better off spending your few Skill points on Influence, Athletics, Stealth than soft capping a secondary combat skill you'll only use when the GM takes away your guns/puts opponents too far out of reach.
And, IMO, Close Combat specialists should go with Athletics and a hand Crossbow loaded with Injection Bolts rather than Firearms. YMMV.
A combat character will also want at least +2d6 of initiative booster (again, Drugs, Magic or 'ware, whatever your deal is). +3d6 if you can at all swing it after covering other priorities.
If you want specific build advise post what you have and someone will be along with suggestions.
Have fun!