I would go slicing if you want to keep Biochem but you wont the mission skill Diplomacy that goes with biochem.
My other suggestion would be Cybertech, Armstech and Scavenging, then you will be able to make greens from the Scavenging in both and will be able to update your armor, barrels and mods as you go. You wont be able to make Blues and Purples without a mission skill.