First you need to know what items you will need to take lessons.
1. The Book for the beginners is Essential Elements for Band Book 1. This method is instrument specific so, for example, if your child plays alto saxophone then you will need Essential Elements for Band Book 1 for Alto Saxophone. The book for the Intermediate players is Essential Elements for Band book 2. Some students will also need a supplemental method: Rubank Elementary Method for Saxophone.
2. A folding music stand. Please spend a little more money and buy a better stand. After teaching music for 25 years I have seen countless $15 stands fall apart after 3 months. Don't get a stand that has plastic pieces connecting the telescoping sections of the stand. Here is an example of a good stand.
Please do not buy a brand new instrument on Amazon for $100. You may as well throw your money out a window. The general rule in buying musical instruments is, if the price is too good to be true, then don't buy it.
The best move a parent can make with young children looking to start lessons is to rent an instrument. I generally send everyone to Music and Arts. I like this company because they are large enough to have low prices and they only carry reputable, well made instruments. Please contact me and we can discuss any instrument that you are considering purchasing from them. Buying a used instrument is very similar to buying a used car. You never know how the previous owner treated it and caution must be exercised in buying used. If you live outside of the Central Ohio area we can discuss the options in your area.
Yamaha (Flutes, Saxophones, Clarinets, Trumpets), Vito ( older saxophones, in particular, that have "Vito made in Japan" are very good instruments), Jupiter (Flutes, Clarinets, saxophones), Azumi (flutes), Gemeinhardt (flutes), Holton (Trumpets), Buffet (Trumpets), Conn (Trumpets), King (Trumpets).