Congrats for her credit building, Is she excited? Pshhh I know I would(and im almost there)
Discover IT $2,600- First Premier MasterCard $1,000- Dillards Store Card $300- Fingerhut Advantage $200
i personally started with a best buy and a macys card. best buy is still joint card with my mom.
it doesnt matter if its a store card or a regular credit card. if she uses it responibly, pays her bills on time. etc... she will be set.
im also 22 and got the best buy card at 19 after being denied on my own for 2 years for so many cards. (but i mean i knew nothing about credit and just randomly applied)
Discover and Chase are pretty conservative with their limits and will usually try to match your existing credit limits (as far as my experiences with myself and my fiancé). Then again her mileage may vary but I would suggest like some have said opening a store credit card, preferably backed by GECRB (Old Navy, TJ Maxx, etc.) My fiancé applied for a TJ Maxx card and Citi Forward (regular version no longer available) early on, received a $1.5k CL on TJX and $3k on Citi. 4 months later increased TJX to $3k, then another 4 months later $5k. She hasn't used it enough lately which is why her latest CLI didn't go through however. Once your daughter gets that limit up then she can start playing around with the more conservative lenders.
edit: My fiancé and I are only 21 at the moment. I started credit building at 18 and she started at 19. Looks like your daughter will have a wonderful credit future thanks to you!
