You've decided to start playing flute? Yay! You are going to have SO MUCH FUN.
The first thing you need to do is find a flute. If you have a teacher already, ask them for help BEFORE you commit to an instrument. They'll be able to help you find an instrument that will fit your needs.
If you don't have a teacher already, here are a few general guidelines to help.
If you want to buy a used flute, make sure you have it checked over by a qualified flute player or music shop / repair tech before you buy. You can get some good deals buying second hand, but if you're not careful, you can end up with an instrument that is broken and cannot be fixed. Ask for help!
If you are looking for a new flute, you need to take the age/size of the player into account.
Students age 6 and younger would benefit from starting on the nuvo Toot, a tiny plastic flute designed for tiny kids. It has simplified keywork, is lighter than a silver flute, and has an attachment for the mouthpiece to assist kids in getting their first sounds. It's very affordable, and the youngest students can usually work quite happily with it for their first 5 to 12 months of lessons. You can even find resources designed especially for the Toot in our Studio Store!
If starting with a silver flute, beginner students under age 10 (and some smaller 11 & 12 year olds) will usually have an easier time on a flute with a curved or waveline headjoint.
If the student is very small (7 & under) a flute like the Jupiter Prodigy is your best bet. With the shortened distance at the top end, it's easier for smealler kids to reach the keys and the lighter keywork and shorter length makes the instrument easier on small muscles. This flute is missing the footjoint, so it will need to be upgraded when your child grows enough to handle a full flute. If you can rent one or buy one used from a local flute teacher, that will save you from having to resell the instrument when your child outgrows it.
9 and 10 year olds will usually have good success with a regular flute with a curved or waveline headjoint, such as the Yamaha student flutes with a curved headjoint or the Jupiter waveline student flutes.
Many music stores have rent-to-own options - check to see if you can rent a curved headjoint flute and put the credit toward a regular flute when the time comes.
Beginner students age 11 & up can usually handle a regular flute with a straight headjoint, such as the Yamaha 200 series (YFL-222 and other 2xx model numbers) instruments and the Jupiter 700 series flutes, both good quality "student" flutes. These student flute will work very well for most kids in middle school and high school.
If there is any uncertainty about brands, models, variants, ask a flute teacher. If you don't have a teacher, ask when the flute specialist will be in at your local music store. You really do want to get the best fit for your child - an instrument that fits the player will make life much more enjoyable; an instrument that is too big is going to make practising much harder work.
Good luck and happy fluting!