Here is a list of items that a classical guitarist would reasonably expect to use on a regular basis.
Nail Care
Diamond dust nail file & 500 grit sand paper: To get a good tone you will need to file and sand your nails. Make sure you get the “diamond dust” file. It looks like powdered sugar has been sprinkled on it. This cuts much more cleanly than the “sand paper on a stick” files. 
Nail clippers (for L. H.) or nail scissors: You will need to keep the fretting hand fingernails short. I like the control that scissors offer. “Swiss Army” knife scissors are great for nails.
Crazy Glue & Sally Hansen Nail Repair Kit: At some point you will break a nail. Don’t laugh, a broken thumbnail to a classical guitar player is like playing a Les Paul unplugged. The crazy glue (“Crazy Glue” brand seems to work best on nails) is for gluing the broken nail back together. The “Mend a Nail” kit is similar to fiberglass and resin. The kit comes with a tissue substance that you apply over the nail (think fiberglass cloth) which is coated it with what appears to be thick nail polish (think resin). The combination of gluing the nail with crazy glue and bonding the area with “mend a nail” will last up to two weeks before needing to be re-applied. The combination of the two is much stronger than crazy glue alone.
Strings
See the article About Guitar Strings for specific recommendations and explanations about the various “ins and outs” of strings.
Spare set: Keep at least one new, complete set of your current favorite set in the guitar case at all times. Your strings know when the guitar shop is closed and wait until then to break.
Dedicated string cutters: Don’t cheap out and buy the ones from the dollar store. Get high quality here and use them only for guitar strings. These are very handy and will last forever if you don’t let other family members get a hold of them.
Tuner
Get a chromatic tuner, not just a “guitar” tuner. Chromatics tuners identify any pitch are preferred because they will read the pitch of the string no matter how far off it happens to drift. Non-chromatic “guitar” tuners look for the pitch that string should be if it is near the correct pitch. They can have problems if the string is very out of tune. Chromatic tuners can also be used for altered, open, and dropped tunings as well.
Three guitar tuner purchase recommendations:
Boss TU12h – The Cadillac of tuners. I have one that has lasted for over fifteen years of daily use.
Korg CA40 – Cheap and effective.
Intelli IMT 500 backlit clip tuner - Clips to headstock. Inexpensive, and works.
Tuner Tips: When tuning the guitar, place the instrument in your lap face up and lay the tuner on the sound board. This will ensure that the tuner gets a good signal through the vibrations of the wood. As the string rings after being sounded, the note goes flat. Always tune to the first attack of the note. Keep feeding the tuner new notes. Always sound the string as you turn the tuning peg so that you can hear the pitch change.
Timekeeper
Metronome – This is a must. If you are buying new, get an electric one that does not beep. If you have one of the old ones with a swinging arm, consider replacing it with a new electric model.
Recommended brands:
Seiko – Nice dial, a bit more money.
Quick tune - Cheaper than the Seiko, but always resets to 100 BPM when you turn it on. Must be scrolled up or down to other tempos.
Guitar Support
You have several choices here. The traditional footstand is easy and cheap. However, it can aggravate problems in your lower back, legs and ankles by holding the leg and ankle bent in one position. Over the years, various alternatives to the footstand have been developed. Most designs fall into one of two basic approaches: a pillow or support placed on the thigh that guitar rests on or a device that attaches to the lower bout of the guitar with suction cups or clamps and has a pad that rests on the top of the thigh. Here are your options:
Footstand: The old standard here. Works well but may not be for everyone, especially those who might have orthopedic problems.
Dynarette Pillow: A crescent shaped pillow that the guitar rests on to achieve the correct angle for playing. The advantage here is that the feet are flat on the floor, it is easy to use and there are no suction cups on the guitar body. The disadvantages are that the pillow is not as stable as the footstand or other devices and it may not offer enough elevation. To see if you like the idea you may simulate this device by rolling up a towel, wrapping a couple of turns of tape around it and placing it on the thigh to see if you like the feel.
A Frame: An alternative to the footstool, this device consists of an adjustable strap that rests on your thigh and a frame that attaches to the guitar with suction cups. The advantage is more stability and adjustment range than the pillow. Disadvantages are suctions cups may damage the finish (especially watch out for French Polish) and it is more cumbersome to use. Several other support devices that work on a principle similar to the A frame are: Gitano, Ergoplay, Effel and Murata guitar supports.
Music Stand
There are a couple of things to consider. You may want a good, heavyweight stand for your home practice space that you can put books and stuff on without having to worry about the thing falling over. Manhasset stands are the standard for this application. For performance you will need a folding stand with adjustable leg height. Don’t buy the garden variety folding stand. Most folding stands don’t have adjustable legs. Guitarists need to have a very low stand so that the audience can see and hear the performer and so that the guitarist is not “blocked “ by the stand.
Manhasset Model #48: Heavyweight classic stand good for home studio use.
Music Stand Pro – Folding stand that adjusts low enough for performance.
In your Case
Try to keep the following in the little pocket of your guitar case.
ID Card: Your name, phone number and address. If someone finds your guitar they need a way to contact you. Take down the serial number of your instrument and if it is a valuable instrument, take good photos of it from several views. Keep the serial number and photos at home.
Pencil: Don’t be flaky. You will need a pencil at rehearsals, gigs, etc.
Spare Strings: See above.
Tuner or Tuning fork: Small tuners will fit, tuning fork always fits.
Sandpaper and file: You never know when you will need these.
