Actually let me go to 'ware. Torso is 1.5 essence, Arm is 1. You could also get Wired Reflexes 2 but that leaves you without room for Reaction Enhancers or much of anything else; you might also go with Restricted Gear plus Move By Wire 2. I could see the following as all reasonable options depending on where you want to go:
Start with Synaptic Boosters 1, upgrade to 3 after saving up enough money in your piggy bank. This has the advantage of letting you jam in a LOT more of the other nice ware like trauma damper, reflex recorders, synthacardium, etc. It will also let you get more cyberlimbs later. But you'll start with 2 IPs, not 3.
Start with Wired Reflexes 2, upgrade to Synaptic Booster 3 after saving up. Cheaper to start, and you begin with 3 IPs, but you will "stall" on 'ware upgrades until you can afford Synaptic Boosters 3.
Restricted Gear + Move By Wire 2. This means you are not going to get much other cyberware; you'll still have room for a little bioware, but not a lot of room. Also eats a Restricted Gear. However, you don't have the above problem of needing to save up a lot for a big-ticket item, you can instead do stuff like get yourself a nicer Alphaware torso, for example.
I would go with Option 2, myself, but YMMV, depends on how much you value power now versus power later.
Now, melee. You will want Blades obviously. Don't get Dodge, instead get Gymnastics - you can boost it with Synthacardium.
You want to jealously hoard your positive qualities for Martial Arts, because they are really good. You have 2 "paths" you can choose:
1) Balanced path. This prioritizes stuff that helps both melee and range combat and is helpful against almost all opponents almost all of the time.
Get Pentjak-Silat (+1 to Called Shots for extra DV), Wildcat (+1 to Called Shots for extra DV), Sangre Y Arroco (+1 Blades DV), Arnis de Mano (+1 Blades DV). If you want, you can grab Kung Fu for +1 to parry defense tests.
For manuevers, definitely grab Finishing Move, Iaijutsu (note that you can draw a FA firearm and shoot a Full Burst as a single complex action!), Off-Hand Training (better than Ambidexterity because it's 3 points only, and does the same thing for most purposes), Riposte, and Two-Weapon Style.
What this is for: fight with a gun in your cyberarm and a katana in your offhand. If something tries to melee you, you still get your full Parry to your melee defense. Against people who try to melee you, you can fight with two katanas, which in addition to looking awesome lets you hit people for about 10P a shot and also get Reaction + Blades + Blades as defense against all melee attacks. You can also blow Interrupt actions with Riposte and Finishing Move to kill people really fast. The Pentjak-Silat and Wildcat manuevers allow you to make Called Shots at +2 to hit; this means you can go from +1 to hit and +1 DV (by taking a -1/+1 called shot) up to -2 to hit and +4 DV. It works both in melee AND at range which is very nice.
Generally speaking, your offense is better with your gun, but when people try to melee you, you can maintain very good melee defense and also good offense with dual wield katanas. Quite a lot of monsters are melee machines (a lot of paracritters and several spirit types) so this is actually pretty useful.
2) Disarm path. Grab Arnis de Mano 3 (Damaging disarm, +1 Blades DV, +1 with called shots to Disarm), Krav Maga (+1 with called shots to disarm), Sangre Y Arroco (+1 Blades DV), Kung Fu (+1 parry), Karate (+1 Full Parry). Take the manuevers Disarm, Finishing Move, Iaijutsu, Off-hand Training, Riposte, and Two-Weapon Style.
How it works: doesn't help you fight at range, but you can cause people some serious problems in melee. Against people who try to attack you with weapons, you use the Disarm manuever to do a wierd full parry disarm thing, if you succeed, you disarm them, deal damage, and you also parried them, so if they don't die you can Riposte them. Against people who are meleeing you without weapons, you use Two-Weapon Style as above for offense/defense combo. Against people who are using ranged weapons, you use the Called Shot to disarm with Two-Weapon Style, and if you succeed you disarm them, do damage, and then if they aren't down follow up with Finishing Move.
This overall is less good when you are at long range, but it gives you an advantage against gun users in close-quarters fighting because lots of gunfighters don't have a good counter to being Disarmed.