It's hard to hide tubing. You can switch to glass or SS if you have the cash, switch everything to the same color (transparent works, but it gets dirty inside), or you can cover the back of the tank with colored paper or paint. As for wires, bundle them with zip ties, velcro straps, or those wire ties that come with bags of bread. You can hide in-tank equipment behind tall stem plants.
To do a complete algae treatment, you can try https://www.plantedtank.net/forums/23...treatment.html
followed by some manual removal after a week or two.
Along with the CO2, you should be dosing, periodically, with macro and micro fertilizers.
It's possible that after clearing out the algae, the ferts and CO2 might be enough to keep it from returning in force, but you may have to raise the lighting or use a dimmer if that doesn't work. Still, the addition of CO2 and ferts should definitely, at least, slow algae growth.
Generally speaking, more filtration is better, and more current is better.
There are lots of "newbie guides" in the form of stickies at the top of every forum.
Good luck! Also, you may want to take pictures. Even if you don't post them here, it's nice to be able to see your progress for yourself. It's easy to forget how things used to look.