By "just the core" do you mean just SR4A, or just SR4A plus Unwired? You really need Unwired to play a technomancer. I'm assuming you do have Unwired and just don't have more obscure stuff like This Old Drone.
You are an orc, right? I can't see it listed but your stats match up and you seem to have Low-light Vision.
What stream are you? If you want to dronomance, you should definitely pick an Intuition stream with Machine Sprites.
2 Reaction vs. 1 Reaction isn't actually going to help you too much; I'd get something else instead.
4 Charisma is fine; you're getting something (more registered sprites) for it. You could go down to 3 and be alright, but it's something that is nice to have.
You really don't want 5 logic. It does little to nothing for you, and you don't need 10 complex forms. You especially don't want to be hardcapping it! I suggest 3.
You really don't want 4 willpower. Even willpower makes Baby Dunkelzahn cry; go down to 3 (you round UP for your stun boxes).
You really, really want Resonance 6. It determines a huge amount of what you do and will save you karma in the long run because of how buying up CFs works.
Infiltration and Perception 3 is karma-inefficient; I'd suggest going 2 and 4, or scraping up 8 more bp for 4 and 4.
Don't buy the Tasking group, because Decompiling is useless. Buy Compiling and Registering separately.
You need to actually buy the Technomancer quality.
Codeslinger is for Control Device, right?
You have waaaaaay too many complex forms. You don't want to have some CFs at 3, either; you want your CFs at 6 because of how buying new ones works. Starting with a 6 and buying a second one to 3 is 6 karma. Starting with two 3s and buying one of them up to a 6 is 15 karma. Also, in general, Technos are good because of their ability to get really high ratings on a few complex forms and being able to thread up "good enough" on everything else.
Cut Browse, Armor, Defuse, and Track. You could take just the 5 remaining CFs at 6. Or you could pick up Disarm. For Cybercombat, you are best off having sprites fight for you rather than doing it yourself; you are simply never going to be good at cybercombat because you are fighting people who just reboot when they "die," whereas you die in real life. If you are really worried about it, the Shield CF is a better investment than Armor.
Gear-wise, what books, exactly, do you have access to? You mentioned you're using a tool - does it have the Arsenal drones and mods in it? SR4A alone is missing a lot of stuff to make rigging functional.