I agree with Pronisias. Yixing is a whole other ball of wax that can get complicated, and tuition can be expensive if you don't spend a lot of time on it. I have a lot of yixing pots that I got when I was new and now never use - at least a couple hundred bucks worth.
IMO it's best to focus on the tea when you're starting out, and then you can start in on yixing when it makes sense to do so. After all, you'd probably regret it if you spent hundreds of dollars on pots only to find that you prefer green tea.
Gaiwans are definitely the way to go until you figure out what you like. Getting a thin one and a glazed yixing (or other very thick) one will cover just about anything you come across and will get you acquainted with the differences in brewing with different materials. While a glazed yixing gaiwan might not do quite as well as a yixing pot, you would at least be able to get an idea of the difference thick clay can make over thin porcelain. You'll also always have a use for the gaiwans, and then you'll probably also find it easier and more natural to jump into yixing pots when you're ready and you know what you like to drink the most.
FWIW, though, my current favorite pot is a $15 one. It doesn't have any collector value, and I have many that are much better made, but to address your original question a pot doesn't
have to be an expensive one to be a good one. There are cheap ones that aren't good, though. They can smell like mud or chemicals or have other undesirable traits.
Overall yixing pots will make a difference, but the difference isn't going to be a mind-blowing one. To get that kind of difference you simply need to learn how to brew; a yixing pot isn't going to magically squeeze every ounce of potential out of a tea. That's just something you have to learn, and while a yixing pot can help you do that you will still have to know how. Even then the yixing pot probably still won't make as much of a difference as it might seem by reading some posts on these forums
