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When you pick up the guitar, play up the fretboard a bit and hold out individual notes. When you pluck a string, you should be able to get a vibration in the wood that you can hear all over the guitar. It should last a few seconds.  The pickups can be changed for very little money, but the wood makes the guitar. Hold a note and listen to the sound decay–does the guitar have a long, warm sustain? Or is it short and metallic? This will depend on the wood and the installation of the neck, which affects the guitar’s sound in a big way.  The guitar should also be in tune in both the 5th and 12th frets. Play up the frets and make sure that a barre chord in first position is in tune, and a bar chord up the scale is in tune. If not, the neck needs adjusted. The scale length refers to the length of the string as it actually vibrates, so it’s measured by the distance between the nut and the saddle of the bridge. The scale can be longer or shorter, depending on this length. What this means for you is comfort. You want to make sure the frets are a comfortable and playable distance apart. Most modern electric guitars are one of two basic scales:  Gibson scale is 24.75 in. This gives the Les Paul its round tone and its hefty bottom end. Anyone who's ever picked up a Les Paul knows the gravity of it. This is partially the scale. Fender scale at 25.5 in. The Fender scale offers a clear and bright playability, great for leads and those Hendrix-style outer space explorations. A 25″ scale is sometimes used by other manufacturers like PRS guitars, offering its own distinctive tone. Action refers to the height of the strings off the fret board. A “high” action means the strings are far off the board, making it require more finger pressure to play each note. “Low” action means the strings are just off the fret board, easier to press. When you play the guitar, pay attention to how far off the strings are and how difficult it is to play the individual notes. Most used guitars will need to be set up, so a certain amount of string buzz can be fixed. If you’re buying a used guitar, though, you need to check for buzzy frets and consider getting the neck adjusted to properly raise the strings off the fretboard to the height you like. You have a number of nut widths, which set the distance from the E string to high E string. The other features the shape of the back of the neck. Primarily, the sound of the guitar coming out of the amp will be made possible by the pickups. When you're first starting out, you probably won't notice a huge difference, or might not care much about the pickups, but it's less complicated than it seems. Learning to differentiate between the two most basic and most common styles of pickup will help you make an informed choice. Some guitars will come with both styles, while others will have one or the other.  Single-coil pickups have a glassy tone, great for blues and rock and roll leads. These will be oval-shaped, and have little metal spots, one per string, under the guitars. Stratocasters come custom with single-coil pickups. Humbucker pickups were designed as improvement to the single coil pickups, giving you more of a growl when cranked up loud. They're rectangular shaped and made of metal. If you plan on strumming and getting some distortion in your sound, you'll likely want a guitar with at least a humbucker pickup. Some guitars will have different kinds of pickups, for example, P90 pickups were the most popular among guitarist, the sound that they have is that mean growl from humbuckers but a warm bass tone along with it. With distortion, these pickups had made a mark on guitar history. The bridge of an electric guitar will feature a number of different designs, some more complicated than others.  Some “floating” bridges feature tremolo bars, also known as “whammy bars,” which allow you to bend the bridge and “dive” the sound accordingly. These can be customized but are standard on some guitars. It's good for some players to notice where the bridge lays in relation to where you hand wants to naturally rest on the guitar. Some guitars look great but have somewhat sharp or awkward bridge-placement, which can make it a challenge to play comfortably. Likewise, some bridges have irritating string-guides, which can make restringing a challenge. It's a good idea to consider these topics when making a selection.
Check the intonation of the guitar. Check the scale length up the neck. Check the action of the guitar. Make sure the neck feels comfortable in your hands. Look at the kinds of pickups used. Examine the bridge.