Here is the tool kit I actually use myself, I don't think you'll need any other pliers for basic jewellery making. It comes in a handy little travel case which I've found useful for taking to craft fairs to do any last minute alterations or repairs. I also love how small the pliers are and, as they fit in the palm of my hand, I find them easier to use than regular pliers. The colour coded handles on the pliers are great for learning which pliers do what.
I haven't actually used these myself as I have never used memory wire, but I shall buy some soon as I would like to start using memory wire.
I used one of these in a jewellery making cafe in Wales, they work wonders keeping all the beads from rolling around everywhere!
Jump rings are probably the most crucial jewellery finding you can get, they attach nearly everything together! Jump rings come in a variety of sizes and colours, even different shapes! They can also be used for chainmail work.
Headpins and eyepins are used mainly for turning beads into charms. Eyepins can be used to turn handmade polymer clay shapes into charms. Headpins are used to make a charm with nothing else attached whereas eyepins are used to make a charm that you can dangle another charm or pendant from.
Chains are used mainly for bracelets and necklaces. I like to use scrap pieces of chain on kilt pins too. It is usually purchased by the metre and there are many varieties available. Pre-assembled necklace chains are also available which would be great to use if you are new to jewellery making.
Earring findings come in a large variety of styles. I personally prefer French fishing wire (called long ballwire/fish hook on Beads Unlimited) and flat stud pads. Flat stud pads can only have flat-backed cabochons glued onto them.
*Beads Unlimited is one of my favourite beading suppliers, the wholesale prices are super cheap and everything is great quality!*