There are so many types of electric guitars; it is hard to generalize which models are the best. I personally like the classic designs of the 50's and 60's. There are two different types which I will talk about.
First, the bolt on neck, single coil fender type guitar. Fender was the first company to mass produce a completely solid body electric in 1952. Until then, there were only acoustic guitars with a microphone on them. The problem was the hollow body created feedback and could not be amplified well.
A man called Leo Fender solved that when he designed and mass produced the first solid body electric guitar called the Telecaster. Two years later Fender introduced the Stratocaster, which today is probably the most popular and copied type of electric guitar there is. Both the "Tele"and the "Strat" are still very popular instruments.
Now let's talk about pickups. The pickups in a guitar are microphones placed under the strings of the guitar to "pick up" the sound of the vibrating strings and send it electronically through a cable to an amplifier where it is amplified.
Pickups generally fall into two categories: single coil and double coil. The double coil is also referred to as "Hum buckers or Hum bucking".
Single coil pickups are very clean and open sounding. This is because they let more of the frequencies come through to the amplifier. They have been generally associated with Fender instruments. The problem with them is they can be noisy in certain environments.
Double coil pickups or "hum buckers" named so because they "buck the hum" were invented by a company called Gibson and are generally associated with them as the single coil is to Fender. Hum bucking pickups place two single coils next to each other. One coil is wired out of phase with the other which filters out some of the high frequencies as well as cancels out a lot of the noise associated with the single coil. In doing this they have a very thick warm sound. Some people prefer one over the other, but most would agree they both are unique and each has its own merit.
A very popular Gibson guitar model called the "Les Paul", which was designed and named after musician/inventor Les Paul. Gibson also makes the SG, the Explorer and Firebird models. Gibson guitars have a glued in neck rather than bolted on which adds to the guitars sustain. The "sustain" of a guitar is how long a note will ring.
There is one other difference between the two types of guitars and that is the scale. The "scale" is the length of the string from the nut to the bridge of the guitar. A guitar such as the Fender has a longer scale length than that of a Gibson. This translates to the longer scale being more taut or stiff than the shorter scale. In other words, a Gibson is easier to bend a string than a Fender which has the longer scale length. However, the fender's stiffer string tension is better for heavy strumming.
Today you can get just about any combination of the two original designs, and there are probably more different models and manufacturers of guitars than there are cars.
When looking at electric guitars for a younger person, durability is an issue. Electrics either have a neck which is bolted on or glued on the body of the instrument. A bolt on neck is the most durable and in most cases the best choice for the beginner.
There are guitar packages that are very popular and are aimed at the beginner or parent who is looking for a guitar for their youngster. In most cases they are the best way to go. They include the guitar an amplifier and all the accessories that you will need to get started. You will need an amplifier to properly hear an electric guitar.
Make sure where ever you buy your guitar it comes with a return policy. If you don't have experience with the guitar you should have someone who is an experienced player, inspect and play the instrument before you commit to buy it.