Love the advice from above to be authentic at an age-appropriate level. The fact that you are connected and so thoughtful about your feelings and reactions to this is such a great sign. And there is nothing wrong with going slow at all! Individual and couples therapy is a great idea if and when you decide to be more of a presence in her life.
This book really helped us with a very similar issue- it lays out the major situations and triggers that can happen in an actionable way. The Stepfamily Handbook:: From Dating, to Getting Serious, to forming a "Blended Family" https://www.amazon.com/dp/172085520X/ref=cm_sw_r_cp_api_i_KTZJFbMT4V6EH?_encoding=UTF8&psc=1
The best advice I can give you is to not try and be her parent, and make sure she has quality time with her dad (especially if you move in). The best gift you can give her is your full, undivided attention. Kids love to be heard.
You need to be sure that this woman is going to be a long-term part of your life before introducing her to your kids. The very worst thing for your daughters is to watch you bring in a revolving door of women into their lives. They are likely still fully acclimating to the divorce, and haven't really thought of what life would be like if you date someone or marry someone other than their mom.
This all on top of your oldest being in a very tumultuous time of life already. Blending families is hardest with teenagers, because teen's brains are WIRED for finding and establishing independence, not for building family relationships. It's the time in life where they say "Okay, I've done the family thing, it's time for me to really focus on my friends and myself" which makes it really hard for a new person to be brought into the mix successfully.
Teens use their strong family relationships as the stable foundation they stand on while branching out and trying new friendships and trying out new identities. If you're in the midst of changing their family foundation, they take it—understandably—not very well most of the time, though they don't necessarily comprehend themselves WHY they are having such a hard time.
All this to say, that this is a big deal, and you and your girlfriend should both read up on as many books about blending families as you can, to prepare yourselves for the years ahead.
Building Love Together in Blended Families is a good resource for both of you https://www.amazon.com/Building-Love-Together-Blended-Families/dp/0802419054
As is Saving Your Second Marriage Before it Starts https://www.amazon.com/Saving-Second-Marriage-Before-Starts-ebook/dp/B00UF72D4O
Highly recommend this book: Surviving and Thriving in Stepfamily Relationships -- I (F47) mom of 2 sons (8 and 12) and stepmom of 1 daughter (16) shudder to think where we (myself and husband (48) be without having shared understandings based on what we learned from reading it.