My daughter is showing interest in bows. I am looking to get her one.
My favorite bow was a Matthews DXT but that was 15 years ago LOL

Any recommendations on a good bow for under $300. I am thinking keep the lbs low until she gets used to it.

I have not bowhunted or shot in 15 years so I have been out of the game for a while.

Mission Craze/Menace  or equivalent if you still want a Matthews bow.

Can’t help as I’m new to archery but I was in the same boat last week. My 8 year daughter had been asking me to buy her one. Having zero knowledge on the topic myself, I decided to go to a local archery range. Counter guy was super helpful and referred me a LGS that has a coach with a shooting team. Dude walked me through the whole process understanding our needs. We ended up with a Mission Radix which is adjustable allowing my daughter to “grow” with it. Spent about 550 for a complete setup ( bow,sight,arrows etc). Daughter did great at her first lesson.

Hoping you got your daughter a bow by now but I'll share my story.  We live outside Gainesville, FL so the Easton Newberry Archery Center is super close, it's a state of the art archery facility.  I took my 10 yr old daughter there over spring break this year and got her an introductory lesson and some range time and she fell in love with it right away.  She's blind in her right eye so we got her set up with a left-handed bow. (I'm left eye dominant so I also shoot left handed coincidentally).   She was pretty darn good right away and I was pleasantly surprised.  
  The next weekend we went to the local farm store that also sells guns/archery equipment.  Got her set up with a Genesis mini compound bow to shoot with.  We've been shooting together at the house on a block target I've had.  It's been great spending some quality time with her and sharing something I love to do also.  Can't wait to get her moved up to a higher pound bow and take her hunting with me!

Get her into the NASP (National Archery in Schools Program).  My son won enough in scholarships to pay for his first year in college.  It is cheap also.

The bows are spec and run about $200.