Battery -- Fully Discharged...

[SoxMan]

My battery on my '03 X5 completely discharged overnight (left the lights on). Never happened before. I jumped it and drove it for 45 minutes. Everything seems fine.

My question: should I re-charge the battery with a re-charger, even though it's already charged to some extent via the alternator? Or, will it just gradually fully re-charge as I keep driving?

I'm worried that I could end up putting stress on the alternator... I just installed a new one last year.

Other option: should I just replace the battery at this point -- it's the original one. If so, any recommendations on after-market brands?

(BTW, I haven't checked how charged it is yet... I know there's a way via the dashboard, right? Assuming it's partially charged at this point...)