I get asked this question on many occasions. In order for me to answer this, let’s first discuss what our options are.
1. Acoustic Guitar.
These are steel string guitars. They produce awesome sound and have a workable neck. They are portable as they produce their sound acoustically and hence don’t need to be plugged into an amp.
2. Classic Guitar.
These are nylon string guitars. They produce a sound that is clean and warm and is in line with classical music. The necks on these guitars are generally very wide. Again it is portable as it produces it’s sound acoustically and does not need to be plugged into an amp.
3. Electric Guitar.
These are steel string guitars. As the name implies they produce their sound by means of pickups which require electricity. Hence these guitars are not portable in the sense that you need to carry an amp and cable around. Generally they have small bodies and narrow , workable necks.
Now that we have a better understanding of the options we have, let’s get into which one you should start with.
If the student is under the age of about 12, I highly recommend a classic guitar. The reason for this is because of the nylon strings. As already mentioned these guitars are fitted with nylon strings, which will be a lot easier on the fingers. Learning how to play for the first time is challenging on the fingers so we want to make the process as pain free as possible for young students. One issue with classic guitars is the wide neck. This becomes a problem when we commence with chord playing and cover certain aspects with chords. Once young students reach the chord level, I generally suggest they progress into an acoustic guitar as their fingers and hands have strengthened.
Under 12 = Classic Guitar.
If the student is over the age of 12, I recommend an acoustic guitar. They produce excellent sound, are portable and have necks that are not too wide. This is especially important for students with smaller hands. The steel strings will be harder on the fingers initially. However hard work and dedication will get anyone through the initial stages of finger and hand strengthening. Fight through the pain. 
Anyone over 12 = Acoustic Guitar.
For students who really want to play the electric guitar, I have no issue with that. One thing to note though is that playing an electric guitar is quite a lot easier on the fingers. This is due to the gauge or thickness of electric guitar strings being a lot thinner than acoustic strings. I would therefore still suggest that these students learn first on an acoustic guitar as this will allow their fingers to strengthen quite a bit. This will then make the transition over into electric a breeze.
I hope that you now have a better indication as to which guitar you should commence with.
Should you have any additional questions feel free to contact me.
Mario