So here's a few tips I learnt along the way, though only from my own experience. It's not a "one size fits all" type of thing, and personal preferences certainly do come into it as you try different types and sizes of wire, until you settle on your personal favourites.
For just mucking around, it's good to play with "artwire" that can be bought cheaply and you won't feel heartbroken if you have to throw it away. I started with a beautiful silver one, though it comes in many colours. It doesn't have the same properties as sterling silver wire, so there is only so much you can learn with it.
Dead Soft Round Wire
This is my wire of choice.
It is very flexible and allows you to mould the wire around a stone, and do twirls and curls if you want. Once you have finished, then you need to polish the finished piece - I just do it with a silver polishing cloth while I watch TV. This hardens the wire and sets it in place, so polish until it's very firm. It's worth remembering when using dead soft wire, that the more you 'handle' it, the harder it becomes. Because of it's flexibility, it does allow you to correct a mistake if you are careful, but not too often!
I have found that dead soft gold filled wire is not as flexible as sterling wire, so be careful not to handle it too much if you can.
Half Hard Round Wire
As the name says, it's half hard, and a lot less flexible than dead soft. This wire is good for creating frames or designs that need to hold their shape, and handcrafted ear hooks.
Half Round Wire
This wire is made with one side flat so that it can be wrapped around a bundle of other wires to hold them in place. It's very useful, though somewhat hard to find sometimes. You can use it as a feature in itself, especially with cabochons.
There is a whole range of specialist wires you can buy from a good supplier. In Australia, the one I use is A&E Metals . I have used a twisted wire, and have tried a sort of cable wire, and hope to try the more specialised ones soon. Used in combination with round wire, as a feature, they can add a whole new look to your designs. They tend to be half hard, and not very flexible, but with a bit of practice are worth using.
Gauges of Wire
The lower the number gauge, the thicker the wire, and the more expensive to buy.
For heavier stones and crystals I use 20g sterling and gold filled wire.
For lighter stones and some smaller raw crystals I use 21g, and occasionally 22g.
For half round, either 20g or 22g, though the smaller gauge is quite small.
If you want to make headpins, 21g is for a thicker pin, or 22g for fine work.
18g is getting more heavy and expensive, but excellent for rigid designs.
For coiling wire I use fine 26g wire around 20 gauge. It's strong enough not to break easily and to support a 'weave'. I haven't tried the finer sizes yet, that will be interesting.
I hope this helps!