Key points above about choosing a good guitar vs. "any" guitar for a beginner. We all tend to think in the $200-$400 range assuming it's the right budget for "starter" quality. I disagree based on some of the following points:
1. New players should be able to learn and feel/hear progress. A cheaper guitar may not permit that due to poor playability.
2. Poor playability leads to quitting since students feel like they're not progressing.
3. Practice times will be discouraged due to poor/painful results. Note that guitars will hurt at first, but as callouses build, that goes away.
Thoughts:
1. Plan on the price of the guitar to not include the case; spending $400 on a guitar "with a case" usually means you're getting a $250 guitar.
2. If you can spend $100-$150 on a case, spend that instead on a better guitar.
3. Know that if you get a very good quality guitar and you choose not to pursue it, you can sell it to get some of your money back. In that thought process, you've rented a better quality guitar than you would have originally bought and still spent about the same amount of money.
Visit a guitar forum and review the opinions of various guitars. Google for specific reviews of the guitar you might be interested in.
One last point about string height - you should be able to adjust the G (number 6/top) string to right at 4mm at the 12th fret. That will result in a very playable guitar regardless of the brand.
Happy Hunting - and in guitar world, be careful of GAS - Guitar Acquisition Syndrome.