To start, balloon twisters typically use high quality balloons produced by reputable companies such as Qualatex and Betallatex, which are specifically manufactured for twisting. These balloons come in a wide variety of colors and you can purchase a bag of same colored balloons or a bag with a mix of colors - typically 100, 144 or 500 to a bag. You can expect to pay about five dollars (US) for a bag of a hundred balloons.
The most popular size balloon for twisting are those known as "260's." There are "fatter" "360" balloons, which are sometimes used by experienced twisters. There are also "thinner" "160" balloons that are used by some twisters, particularly those with small hands. Most of the standard sculptures are geared towards the use of "260" balloons.
Balloons that can support your twisting come in a wide array of shapes and sizes for specialty sculptures, which include: traditional-shaped oval balloons, which can be used as a head or eyes in some creations; heart-shaped balloons, good for topping off hats; bee-body balloons and many more.
But when you're starting out, you'll find that 260-size balloons will serve most of your needs. Balloons for twisting can be purchased from a variety of online sources.