The best screen protector I have found so far is a case friendly film one from Armorsuit, and I got it off Amazon for around $7.
It's not perfect as it has a slight 'orange peel' effect and it's a bit squishy with the stylus, but it adheres to the edges, which is the most important thing for me. My mother got the Armorsuit matte version which also adheres well (and isn't squishy and doesn't orange peel!), but as it's matte, the screen resolution is reduced.
I've also tried 2 case friendly IQShield Liquidskins that had a prominent orange peel effect and did not adhere to edges well at all. I also tried a flat tempered glass, Spartan XtremeGuard, that haloed on install and was very narrow and jarring when swiping from the flat part of the phone to the edges and vice versa. I wouldn't recommend either of those, personally.