The gallon is a great starting size. With that you'll get at least several bottles (depending on what bottles you use) so you can taste it at different amounts of aging time. There are many in the brewing world that don't like the slogan 'mead gets better as it gets older', but I've always preferred aged mead to young mead.
For a 1 gallon batch, I would go with around 3 pound of honey. You can add a few more ounces if you want to start breaking into the semisweet range (this will also depend on the alcohol tolerance of the yeast you use). On the subject of yeast, you can use something as simple as bread yeast. But I would recommend this:
https://www.morebeer.com/products/icvd47-dry-wine-yeast-5.html. It works well for mead and is one that I use pretty regularly.
You'll also want to get something to act as a nutrient. You can use any nutrient that would be used for wine. This is the one I normally use:
https://www.morebeer.com/products/fermaid-yeast-nutrient.html. A 1 gallon batch should only need around 4g of nutrient.
Your basic rundown will be something like:
- Boil your honey.
- Stir in water to dissolve it. Nutrient can also be stirred in at this time.
- Let it cool down to about 70° F.
- Move it to the fermenter and pitch the yeast.
While fermenting, CO2 will escape. If you don't have an airlock and stopper with the equipment you got, you can use a balloon over the fermenter. You'll just need to let the gas out periodically. And last but not least, keep everything as clean as you can to prevent infections. If you think you might make more than one batch, it will be worth picking up some sanitizer.
Good luck! And I'm happy to provide any more input if you need.