I am enjoying Arkham Shadow and want more Batman in my life. ok to play this?

Okay, so like a month ago I got Batman Arkham Asylum and I need more Batman games. Can someone tell me the chronological order or that doesn't really matter?

Hey, so has anyone noticed this bug were after completing a challenge map you will always get "New Personal Best" even if you didn't beat your old score?

Is he stupid?!

I never played #2 or #3 but going to after redoing this one but I forgot how well designed and genius this game actually was and still is today lol I'm having a blast playing it again I originally played it on console but the PC version is awesome. Except having to play in BPM cause the keyboard controls are horrendous. Still I forgot how fun it was to play this game lol...