If you play rock or heavy metal music and are using an acoustic/electric guitar for ballads or quieter songs, you will want to use at least 10-gauge strings. Most guitarists playing this type of music tend to play a bit harder and faster than those in other genres, which can cause strings to break and fall out of tune easily. If you play particularly hard, or with a heavy gauge pick, consider using 11 or 12 gauge strings to prevent broken strings and tuning problems. Some guitars may need a wider nut to hold 11 or 12-gauge strings, but replacing or widening the nut is a simple procedure that any luthier or guitar technician can perform.
Jazz guitarists often play acoustic/electric guitars during live performances with both their fingers and a guitar pick at different times, often within the same song. Jazz players generally use 10-gauge strings because the strings have a wide tonal spectrum, but some jazz guitarists use 11, 12 or 13-gauge strings if they employ heavy pre-bends or vibrato in their playing. Many jazz musicians use flat-wound strings instead of the more common round-wound type used by most, because they are a little bit easier to fret when playing complicated chord inversions that often appear in jazz music.
Classical or Spanish style guitar players must use nylon strings. If a guitar is meant for classical or Spanish style, you do not want to use steel strings on the instrument for any reason. Steel strings will not stay in tune and they will warp the neck of your guitar over time due to increased tension. Nylon strings come in a ball-end variety like most steel strings, though the more traditional nylon string makers do not manufacture strings with a pre-made end. Some players prefer the authenticity of traditional strings, while others appreciate the ease of using ball-end strings. String gauges vary for nylon guitar strings like regular steel strings.
The most important thing to consider when purchasing strings for an acoustic/electric guitar is personal preference. If a certain string gauge or brand feels right then it is. The only way to find the best strings is through experimentation. There is no right or wrong answer, only what feels and sounds the best to each individual player.
If an acoustic/electric guitar is going to be used for live performance, 80/20 bronze strings are often recommended, as they tend to have longer life than many other strings. Elixir, Martin, Fender and D'Addario are popular manufacturers of this string type.