Acoustic guitar might be a cheaper option however; the electric guitar (in my opinion) is a much better starter guitar. This is due to the fact that acoustic guitars usually have strings with higher tension that make it harder to press down on the strings. The action (how far the strings are away from the fretboard) is also much higher which also adds to the difficulty of fretting a note because you need to put more pressure on the strings than an electric guitar. This can be especially frustrating for beginners who have not built on up calluses on their fingers to withstand pressing on strings for long periods of time.
I have also had students who have had problems reaching chords on an acoustic that they were able to grab much easier on an electric. On an acoustic guitar the frets are larger, and this can be extremely challenging for children starting out who have small hands. This is ultimately your choice however and starting on an acoustic is not a bad thing to start out on if you practice enough. I recommend children start on the electric especially if they are into rock music as it will keep your child motivated to play in the long run if things are a little easier to learn starting out.
A folder- This is preferable, so you can keep track of any music material I printed out for you. Usually, I hand out papers with topics we discuss in lessons; this can be useful as a reference to previous material while practicing.
Tuner- This useful device will help you to accurately tune your guitar strings to the correct pitch; it is also useful for experimenting with different types of guitar tunings. You can find multiple free tuning apps for download on either Android or iPhone. These can also be found at any local music store for as cheap as $7-10.
Picks- Having your own guitar picks is important for practicing strumming and right-hand technique. Buying a pack at your local music store would be ideal. I recommend experimenting with different pick thicknesses to see which picks work best for you. Thin picks with a round edge can be useful for strumming chords but can make it harder to pick smaller motions and keep the pick controlled. Thicker picks with a sharper edge can be good for faster playing or for styles that might require smaller picking motions.
Strings- Extra Strings are always good to have as a backup just in case you break one. Eventually you will want to replace all of your strings yourself because eventually the worn strings will start to sound bad. You can also experiment with different gauge strings depending on the type of music you are playing. Thicker strings might sound better for rhythm playing and chords but if they are too thick they can make soloing harder on your fingers.
Wire Clippers- Buying a pair of these can be useful for changing strings so you have something to cut your old strings off easily and replace the strings at a faster more efficient rate.
Tuning Winder- This is a great tool you can use to rapidly detune and tune up your guitar strings when changing them to make the process a lot faster a more efficient.
Polish- This is entirely optional but will keep your guitar body looking clean and presentable
Strap- This is good to buy early on especially if you plan on playing with other people. It is a good idea to practice standing up if you plan on performing in front of a live audience.
Music Stand- This is completely optional but is good for holding your papers up so you are not hunched over while playing which could lead to unnecessary pain and discomfort in your shoulders, back, and arms.
Amplifier- If you have an Electric Guitar this is essential to buy so you can hear your playing clearly. If you are just starting out you can buy a cheap amplifier between $20-100. Craigslist can be a good source for great deals but be careful to check the amplifier before you buy it so you know for sure that it works properly. Fender, Line 6, Orange, Marshall, Peavey, and much more offer small amplifiers that are relatively cheap that you can find in any local guitar store.