If this instrument is for a child, let's say under 10 years of age, you should consider a smaller bodied guitar, 1/2 to 3/4 size with nylon strings. The nylon strings will be easier for them to press down and the smaller body will allow them to play in relative comfort. You should expect to spend between $70-$90 for one of these instruments.
If this instrument is for a teenager, well, you will be the best judge of what instrument to purchase. Being honest in your assessment of your child's tendencies may save your hard earned money and some poor teacher's sanity. If your child tends to start "things", then stop after a few weeks and move onto the next "thing", you may consider renting an instrument before you buy. Guitar rentals should be around $20-$30 a month. Find a store that will  apply your "rental fees toward purchase", in case you want to buy an instrument a few months down the road.

The 3 Basic Guitar Categories:

Although not usually considered the number one choice for first time buyers, entry level electric guitars have enjoyed a huge increase in popularity over the past 5 years and have become a serious contender in the "first time buyer" market.
The quality, selection and value of entry level electric guitars has never been better!
The down side being that virtually all electric instruments require some sort of amplification and that means added costs. However, to meet the demands for more affordable electric guitar/amp combos, most major manufacturers have put together "packages" which contain everything you need. I mean everything!
Guitar, amplifier, cable, gig bag, picks, instruction booklet... some even include a video and electronic guitar tuner, even a spare set of strings!  A good quality electric guitar/amp package will cost between $275-$350.

Also known as "dreadnought" guitars, (for their body size and shape) are the number one choice in the current guitar market. The reason is simple, these guitars allow a player to perform a wide variety of musical styles. From rock, pop, jazz and country, dreadnought guitars are extremely versatile. The quality of entry level acoustic guitars have improved greatly over the past ten years. This is mainly due to the commitment of major guitar makers like Ibanez, Gibson/Epiphone, Fender® and Alvarez competing for the entry level market. Finally chalk one up for the consumer!
You should expect to pay between $175-$275 for a good quality entry level acoustic guitar.

The entire SDG series from Suzuki Guitars are a great choice for the first and second time buyer. Quality woods and hardware define the Suzuki line. Prices start under $150. A definite top contender in the field!
(Soon do be discontinued)

In the past, classical guitars were reserved for exactly that, classical music. But these wonderful instruments have also enjoyed a surge in popularity due mainly to the success of various ethnic music styles. Although not as versatile as the dreadnought, classical guitars are an excellent choice for Brazilian, Latin, Spanish, Jazz and of course, Classical Music.
A good entry level classical will cost you between $175-$275.