I was starting to have a little fun with this character and I was wondering if I could build decent character without using any Ware or Magic.
You're gonna need a lot of Edge to spend on the Blitz option to roll 5d6+(INT+REA), since you won't be able to rely on ware or spells/powers to get multiple initiative passes. And those are the bread-and-butter of combat characters; like in virtually every game, if your side dominates the action economy, you're more likely to win and take less damage in the process. By the same token, you will be even more dependent on getting the best possible gear that gives dice bonuses that might otherwise be provided by ware. But even with a smartlink you won't be rolling as many dice as someone with cybereyes, just because of how the wireless smartgun rules work.
Since you're going to be maxing your stats at the natural max, your pools are going to be lower for everything - for shooting, for dodging, for base reaction, anywhere from 2-4 depending (and even more for Reaction compared to Wired Reflexes + Reaction Enhancers). So you may need to be more environmentally aware (of cover, hiding, situational modifiers and things to give you an edge in combat) which other characters might overlook.
You may want to look into drugs, which can temporarily replicate some of the bonuses of ware (roll more d6s in initiative, +s to stats, etc) but they can come at the dangerous cost of addiction checks.
I think it's doable, I don't know how I would allocate priority to be honest. Magic E of course. You'll need some money but much less than someone buying a ton of ware. You'll probably want a decent Edge and high Attributes, and invest heavier in Specializations to key skills like your main combat skill.
