To answer your more general question:
Needles are supposed to be in standard sizes, either in US sizes (the smallest are several zeroes and the biggest are double digit numbers), or UK sizes (the reverse sizing method of the US), or millimeter, which is the measurement of the diameter of the needle. So if you get 3 pairs of needles and they are all a size 2 US (which is size 12 UK, or 2.75mm) and one pair is made from aluminum, one from bamboo and one from plastic, they should all be the exact same size. However, because of the way yarn grips or slips on different materials, and an individual knitter’s style, they may produce different results. Also, which yarn is used. The general rule of thumb is that you should use a grippier needle (say, bamboo) for slippier yarns and a slippier needle (metal) with grippier yarns.
There is also the factor of personal preference. I cannot stand to knit with plastic or acrylic, but some people love it and will use nothing else.
The different types of needles- straight, circular and douple pointed, are used for doing different things, and again, personal preference comes in here, as well. If you have long enough cords on your circulars and use something called Magic Loop knitting, you can actually knit any size of flat or round knitting. I personally do not like ML at all, and so I use DPNs for small tubes, such as socks, mittens and cuffs. Some people use their circulars for all flat knitting, but some prefer to use straights for that.
As others have said here, to get the correct gauge, use the size needle that works for you. I usually go down a couple of sizes to get the correct gauge-- I’m a very loose knitter. But I have a friend who is a tight knitter and has to go up 2 sizes. In patterns, they’ll give you a needle size and that’s really just a suggestion. (If they give you more than one size, you do need to use 2 sizes, because they want a tighter and looser knit for different parts of the project.)