So, you're interested in the idea of distilling eh? Great! Now, first a disclaimer, technically distilling your own liqour is illegal. That being said, now let's talk about what's involved, and what you need to do it!
First off, you need to make a mash. What's a mash? It can be as basic as making up a bunch of water and sugar and tossing in yeast, or you can do say a molasses and cane sugar route, then add some craft distiller's yeast. So, how to decide on what style mash to make? Well, first you need to decide what equipment you'll use, and that should help make your choices easier.
To keep this simple, we're going to compare the Reflux and Pot stills.
Reflux is going to give you very high alcohol content, but give you a very neutral spirit like vodka. So, it doesn't matter what ingredients and flavours you put in your mash, because a reflux still is designed to strip out all impurities (which a lot of flavours are), it's going to leave you a very high percentage, but flavourless spirit. That being said, you can buy tons of different flavourings to make your spirit taste like many of the different whiskeys, bourbons, rums, gin, tequila or even cream liqeuers.
Pot stills however are the opposite. They're going to give you a mid range spirit, but retain all those delicious flavours you tossed in that mash with the craft distillers yeast. You can get the high alcohol percentage from these as well from running your spirit through it again, though you will lose some flavouring doing it that way. This is more for the person who wants to get creative with ingredients, and possibly come up with the next great idea for spirits.
With either of these still tops, you'll need a boiler. There are simple boilers, like the T500, or if you're already making your own beer with a Brewzilla or a Grainfather, you can just get a stainless or copper lid for them, and then attach whichever top to it and go!
As far as the stainless vs copper, copper will give you a smoother flavour in your spirit. Stainless however, won't tarnish and is super easy to clean. So it really comes down to what your end goal is, and what all you brew!