I've played guitar for 40 years now and I am always appalled by the guitars out there that are primarily designed to rip off the buyer.  Let's talk about used guitars first.  First and foremost, take someone knowledgeable with you to check it for you and play it.  Sight along the neck as you would a rifle sight and make sure the neck is straight. The strings should be consistently low to the fretboard (this is called "string action.") .  If the strings are high towards the soundhole, the guitar has a warped neck and you shouldn't buy it. Believe nothing a music shop owner tells you about the guitar and always offer a much lower price.  Negotiate.

The fretboard should be made of rosewood and the strings should ring clearly when you press the string against the fret.  If you hear buzzing noises or a dead sound, don't buy the guitar.  Check to be sure that the top is made of a good spruce or mahogany or other quality sound wood, rather than plywood (often these have a faux decal or laminated veneer finish).  Good wood leads to good sound.  The pegs (preferably true metal machine pegs) should work smoothly without any "give" or sloppiness.  In other words, you should be able to tune each string in small increments.

Steer away from old arch top guitars from Sears (Silvertone) or Harmony.  These are bad guitars and very hard to learn on.  Yamaha and Takamine make good low end priced guitars and have held up fairly well as used guitars.  If you are going to pay a little more, look for a used Gibson (my personal favorite) or if you are a diehard folkie, an older Martin.  Used guitars often sound worlds better with new strings.  Beginners will do well with Dean Markeley light bronze wounds as these strings are easier on the newbie's uncalloused fingers.  You can graduate to heavier strings when you know more and your fingers are tough..

If you are buying on Ebay, ask questions such as:

--Is the neck straight?

--What is the serial number and make of the guitar? (all reputable guitar companies can tell you when and where each guitar was made based on the serial number of the guitar, located in the sound hole), and you can then in turn, check with the company or online to double-check the seller's information.

--Will the seller allow you to return for full money back if you find the guitar unacceptable?

--What type of pegs and in what condition are they?

--Has the guitar had work done and by whom? Does the guitar have any cracks?  Is the bridge in place and in good condition?

--Does a case (preferably a hard shell case) accompany the guitar?

--Has the seller played the guitar and what is its sound, compared to other guitars he/she has played?

These same questions pertain also to brand new guitars.  Paying a little more for a quality guitar is ultimately better than going cheap and getting a crappy guitar that you or your children will find discouraging.  If you go to Guitar Center or some place like it, negotiate.  Again, take a knowledgeable person with you.  I have actually seen better and more realistically priced guitars on Ebay than in music shops, and actually, better and more honest sellers.

Remember, good guitars are like good tattoos: you get what you pay for.