Until recently, my only experience of tequlia had been tequila shots and the 'lip, sip, suck' (salt, tequila, lime) drill. I didn't know that shots typically used just one type of tequila, and that there are other types with different types of flavours.
Silver (or 'white') tequila is what they normally use in shots. Silver tequila is un-aged and has a rawer, more vegetal taste. All the other types are aged.
There's Reposado which is aged for less than a year. ~AUD$40-50 upwards
Añejo which is aged for one to three years. ~AUD$70 upwards (often over $100). There's also an Extra Añejo category, which is aged even longer.
Gold tequila (known as Joven or oro tequila) is a mixture of a silver tequila and an aged tequila.
Reposado tequila has a nice smooth, earthy flavour. I reckon it goes best 1:1 with some soda water. The slight bite of soda water suits it (soda water is preferable to mineral water, which is preferable to still water). You can also sip it straight. Of those I've tried, El Espolon is my favourite, el Jimador is decent, and I'd steer clear of the Sierra reposado - it's not very nice.
I haven't tried an Añejo yet, but presumably it's similar to a Reposado.
I find Silver tequila goes well with generous amount of soda water and a dash of lime juice, or with tonic water.
Watermelon wedges soaked in Reposado tequila tastes great!
If gluten is a problem for you, good quality tequilas are 100% gluten free. Tequila is made from the blue agave plant, and the good quality tequilas will say "100% blue agave" on the label - these are completely gluten free. If the label doesn't say that, then the tequila will be a Mixto, which includes other ingredients, and these mightn't be gluten free. More info.
Oh, and this is what blue agave plants look like:
Wikipedia page on tequila