This is going to sound funny but right now the most important thing you can do is teach her how to sit down. I'm so serious! If she doesn't know how to get back down and she pulls herself up in the crib, she will probably cry out for help to get back down and you don't want to have to be making that trip a gazillion times a night.
Play ring around the rosie with your child (obviously you can't play the full game). Sing the song and when you get to the "we all fall down" part, gently bend her knees, help her drop her little booty on the floor, and then clap/cheer/sing/praise so she'll repeat the behavior. You'll sing it so much that you'll never want to sing the darn song again, but eventually she'll learn what to do when it is time to "all fall down", and she'll be sitting on her own.
Not only has she learned a new skill; she is now also seeing her world from a different perspective. No more views from the tummy or the back! No more only looking at things at 'sitting level', no sir - now she gets to see what her world looks like while standing. That's fascinating for her.
While there is no need to 'push' her to walking, continue to encourage and support her but ALLOW her to get frustrated, but obviously not to the point of a mega-meltdown. The frustration with not being able to do what she wants to do will give her intrinsic motivation to try and figure out how to move, how to walk, how to stand for longer periods of time. She is developing gross motor skills and problem-solving all at the same time, plus she's working on figuring out her little piece of the world all on her own and wow, I bet she'll be so proud when she does it!
Follow her lead, continue to support and encourage her, and just let her have fun with this new 'trick' she's learned. What an awesome little kiddo!