Where to go from just meeting a girl and having brief chat (more below)?

SirFinkle
I recently introduced myself to this girl I have been noticing in the hallways and at lunch (high school). It lasted about 20-30 seconds (made it short and simple). I know her name and grade and she knows my name. Now for the question. How should I approach her again? Should I do it at lunch (I don't think that is wise until I know her better) or talk to her when opportunities in the halls arrive (again I don't think this is wise because we only get 5 minutes per period switch) or chat with her at her locker before or after school (iffy because I don't know the best way to be like "hey can we chat at ur locker " or something like that) or obtain her number and text to her. Keep in mind I have only known her name and grade since today. I told myself before talking to her that the world will not end if anything wrong happens ( like her looking like she's not interested) and worked up the courage to ask her for her name. Another note she does not have a boyfriend as I found put recenty by talking with one of other "girlfriends". And finally she literally sits right across a main path at lunch at a different table. Like 15-20 feet distance or not even. Thank you for reading this and I hope to get a reaponse. :)
Updates:
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*Thanks Alerathla
Where to go from just meeting a girl and having brief chat (more below)?
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