Different types of lube have, first and foremost, a different chemical makeup.

Water-based lubes are, well... water-based. They're the standard works-for-everything lube. They come in different consistencies, from runny to gel-like, so be sure to read reviews to see how previous users describe the product. Many common water-based lubes that you find in drug stores contain glycerin (and parabens and phthalates) which can irritate some women. However, there are an increasing number of lubes that do not have these ingredients. For example, my favorite water-based lube is Maximus. It's got a great, thick consistency, doesn't contain irritating ingredients, and won't break the bank.

Silicone-based lubes have a different texture than water-based lubes. Where water-based lubes tend to dry out after some period of time (some kinds even get tacky), silicone lube tends to be oilier/silkier in texture and leaves no unpleasant residue. While you can clean up water-based lube with just plain old water, silicone lube requires soap and water. If you're leery about using soap on your bits though, it's fine to just use warm water. Whatever's left of the lube won't trap bacteria against your skin like oil-based lubes will, and will be flushed out of your system naturally. The only drawbacks to silicone-based lubes are that most silicone toys are not compatible with them, and most silicone lubes that I've tried tend to be too thin for anal penetration. My favorite silicone lube is Better Sex Essentials silicone lube. Good quality, cheap, and you get a fair amount of it.

I've never tried oil-based lubricant, so I'll leave that to someone else to explain