Archery is bad yo. Burnout I can't ever figure out why you would want enough cyber to make it worth while to take. I guess if you get your arms blown off and have to replace them with cyber ware, sure, but as a char gen choice? Pass.
Archery's not bad. Just different. Sure, it's noticeable. Aren't shotguns, sniper rifles, and assault rifles too? Plus, Archery has access to some pretty badass arrows. I wouldn't ever run normal arrows. Incendiary, Narcoject (Injection) Arrows, and Stick-n-Shock are all amazing.
As for Burnout's Way, there are plenty of situations where you can get enough cyber. It's mostly long-term stuff though.
1) 1200 Karma I would say go for it. Max out Charisma and Softcap that Agility. You can opt to neglect Strength, and probably Logic. I wouldn't do both though. Also, don't go Bow if you drop Strength.
2) I recommend Unarmed Combat for Close Combat; mainly for Shock Gloves. Those things are wonderful. If you're going to pick up Automatics, Archery isn't helping you. I'd say stick with one or the other. You can throw in Pistols or Longarms if you
really want, but running 2 (possibly 3) combat skills is going to run you out of Karma really quickly.
3) First Impression. Mentor Spirit. Catlike. Blandness. Bilingual. All good choices for positives. Negatives are up to you.
4) Burnout Way is going all the way. Like,
all the way. I mean dropping to just above 1 Essence, maybe 2. Burnout's Way is also incompatible with Used 'Ware; Standard 'Ware is the only one that gets an Essence reduction. If you really want any technological upgrades; Used Tailored Pheromones 3 + Datajack + Smartlink is where I'd start. If you are willing to drop 2 Essence, pick up Used Muscle Toner 3.
Really though, other than the 1 Essence combo above; I would pick up Magical bonuses. Improved Reflexes 2 is always a good start; you aren't going to be the best combatant, as you are dual face/combatant. Level 2 is good enough for that. I would pick up at least one level of Voice Control, go for broke on Authoritative Tone, and one level of Combat Sense. Anything other than that is pretty optional, although some of my favorites are Motion Sense and Rapid Draw. If you want any more powers, consider picking up a Qi Focus. I would recommend putting the activated or situational powers in there, as you can activate the focus when needed. You don't want things like Combat Sense in there, as you want that one always on.
5) Armor Jacket + Ballistic Mask + Assault Rifle of choice (AK-97/98, usually) + sidearm. There might be other things in there, but that's probably a start.