I had glasses from about the age of 8 or 9. It was the end of 3rd grade. I won't say I was 100% responsible, but I did do well with them. Losing them meant not being able to see.
I would start with the pediatrician and just ask if he/she knows of any children's vision programs in your area, not necessarily see the pediatrician. Just ask for info. You can also see if WalMart or another vision center like that would provide glasses inexpensively. You can get the prescription one place and look for glasses somewhere else. I feel that transitions lenses are not necessary, but you want plastic (or flexible metal) and scratch resistant coating.
I went to a local optometrist when I was a kid and I've been to LenseCrafters as an adult. It wasn't bad to go to LenseCrafters, but I never got the same person twice. If you go to a standalone optometrist, you can build a relationship. You may also find it beneficial to go to a pediatric optometrist. Many insurances have a vision component that covers or partially covers glasses. You might also have benefits under AAA membership or similar.
Get her vision checked yearly, especially as she grows. Nobody will sell you glasses for a prescription more than 2 yrs old. Her vision should stabilize when she's older, but expect glasses every year for a while. If she ends up with a strong prescription, try to buy the high density lenses. It will make such a difference.