Wire is wire - right? - - yeah - right! -- like it's that simple.
Wire is made from different materials and in different thicknesses to do different things. You need to think what you want your wire to do - and then choose what will do the job.
The easiest to explain is aluminium wire. Aluminium wire is made from exactly the same stuff as your aluminium foil sheets in the kitchen. it is soft and bendable - crease-able and flexible and can be worked and reworked until you are happy with the shape. It comes in several thicknesses - I have never seen it thinner than 1mm - usually 1mm / 1.5mm / 2mm - but can go thinker for large model sculpting. It does come in loads of colours - it is usually a coloured plastic film coating which will scratch and distress if want it too. It is perfect for sculpting shapes - commonly used under paper mache figures or in mixed media / floristry where you want to sculpt an intricate shape - also as the backbone for wire wrapping. It won't hold it's shape in heavy use or if you put any weight on it.
Next we have copper based. Comes in loads of colours - usually a plastic coating as before,This can come as a thin copper wire which is very flexible and is mostly used for the detailed weaves in wire wrapping - also to add beads to larger pieces and for mixed media pieces to add coils and swirls and texture - and for wire crochet and knitting - yes really!
Now it gets a bit more complicated. You can add other metal too and make stronger wire. The stuff used for making jump rings - ear ring wires etc is a copper base - treated differently and with other things added to make it harder and more resilient - it comes in a huge range of different thicknesses - called gauges - for different uses. This one is much harder to work into shape - won't easily forgive you if you make a mistake - but will hold its shape and take a bit of weight. You can make your own jump rings for chain mail and Byzantine work - but I won't confuse you any further today - we will think about gauge and work-ability later.
Think about how soft and workable you want your wire to be.