I don't think its been on long enough to say what I would do differently but here are some of my ideas:
Ollie brought Diggle into his being Arrow. And he has enlisted Felicity Smoke a few times. I think he should begin building a team, even if the team doesn't know they are a team or about one another, and have Roy come in as a Weapons/Tech expert/dealer. He gets Ollie higher tech weapons and body armor, Ollie's Arrow starts wearing goggles with night vision lenses options, and using "trick arrows" like flash grenade arrows, net arrows, smoke arrows, and electro shock arrows. Thanks to Diggle (who maybe brought Roy to Ollie) Ollie's Arrow becomes more non lethal. But he never looses his edge, like shooting a guy to a wall with an arrow through his hand. He just stops killing. (This could also bring Arrow into conflicts with morality when he then frames the criminals with evidence, something to ensure they get in trouble. Just my own idea there.) He also starts calling himself Green Arrow and becomes less of an urban legend. Maybe in a well calculated plot by Ollie to start scaring his foes in the city. And just for fun to disguise himself while being Arrow he has a fake goatee (spelling?). This would help hide his identity, the Arrow vigilante has a goatee and Ollie doesn't. Ollie should also start showing his political side, and maybe start using the term fat cats. And on that note, Diggle also pushes Ollie into protecting the innocents of the city rather than hunting the names in the book. He still can go after them but he sees how he must put the citizens first.
Meanwhile Ollie begins opening up more to his sister Thea. It starts when Ollie decides that Thea needs some self defense training. So he trains her himself in combat and archery. He starts opening up about what happened on the island, at least half truths and what he can tell. Leaving out other parts and still leaving the drama of him not opening up to his family while still having him open up and get closer. Further in Thea inadvertently meets Roy Harper who has been in the area a lot lately. They start dating, despite Ollie's threats and warnings, and there is now the Roy Harper/Speedy relationship. Later in that same storyarc Thea stumbles onto Ollie's being Arrow, perhaps in part thanks to Roy. (Perhaps her meeting Roy and dating him can come after her falling into Ollie's secret Arrow life.) She never becomes a sidekick vigilante, but just someone who knows Ollie's secret. Maybe helps make up excuses for him.
So now, in the series, Ollie's Arrow has a team of operatives (soldier John Diggle, computer expert Felicity Smoke, and weapons expert/dealer Roy Harper.) Arrow also has higher non-lethal tech and weapons, and a costume/armor upgrade or sorts. His sister Thea would be more important on the show knowing his secret and giving Ollie someone close to talk to and eliminating some of the "Ollie is a jerk, he doesn't care about anyone but himself" stuff. It would also open up the possibility of "Speedy" in the future. And maybe a possible future story where, because Thea is too close, she gets killed or hurt sending Roy into conflict with Ollie and pushing Ollie over the edge back into killing. But that is just a possibility.
On the Laurel Lance front, I would have her begin to transition into Black Canary more. Start showing her at self defense class more. Show her defend herself against a mugger maybe too. And show her views of justice start to be questioned and put her in conflict with her father more. She maybe starts seeing how the vigilante works better than the cops, or maybe she can find out her father is surrounded by crooked cops or could even be part of it somehow. And in a later down the line story he could get killed while trying to go by the book when the vigilante way would have kept him alive. This would give her reasons for becoming a vigilante and show she has the training to start it. Maybe Ollie even starts training her more once she comes to him for help.
I'd also start bringing in enemies that reflect Ollie more, help explore who he is and who is becoming and could become. Someone like Manhunter or Azreal. More stylized costumes and less toned down costumes too.