Haven't read Deathstroke but I've heard the series has become pretty damn good as of issue 15. Also, Green Arrow is getting a new (good) creative team this month, so I recommend you check that out as well. And no, I'm not recommending Batman because you were probably going to read that anyway.
Oh, and there's Red Hood and the Outlaws too. I don't like that series so I can't recommend it, but some other people do and since you're a new reader you may like it as well.