Indeed, a 3 piece airlock and drilled rubber stopper cost a combined $2 at my LHBS. Well, worth the cost especially considering they last indefinitely.
You can use pure (unscented) bleach as a sanitizer as its cheap and widely available (just be sure to rinse very well after sanitizing).
Also, be on the lookout for 1 gallon jugs. You may be able to find these at yard sales, recycling centers, or from friends. They can be bought from hombrew stores for about $3-4 or filled with apple juice ($5) or cheap wine ($9?).
You'll want some food-grade plastic tubing (maybe 3-4') to siphon the finished mead into bottles. You should be able to find this for really cheap at a hardware store. Later you can purchase a racking cane.
If you decide to purchase some advanced ingredients that you can't get locally, you can probably find a Homebrew shop on the web from your state. You can make mulitple purchases at once to save on shipping. And if you want to obtain some quality wine yeasts (about $1/packet) you can stock up, they should keep for a year in the fridge.
I definitely recommend previous posters' suggestion to try Joe's Ancient Orange recipe. It requires only a gallon fermenter with airlock, some bakers yeast, 3.5 lbs honey, and orange, some raisins and some spices. You might also try a cyser (or apple mead). Simply use 3/4 gallon of apple juice and 1-3 lbs of honey (depending on level of desired dryness/sweetness).
Best of luck!