You should immediately start thinking about tea equipment according to different varieties of tea. A yixing pot will be much better suited to Pu'er teas than would be a testubin. That's a pretty radical example, but even so, the idea is that as you get higher quality teaware it will better tailored to certain kinds of tea.
That said, first consider an electric kettle of some kind. I had a $30 one from Braun which I loved dearly, but retired in favor of a Zojirushi water heater which is pretty heavy equipment for a newbie. So go get a competent electric kettle, preferably with an adjustable temperature setting - different teas need to be brewed at different temperatures.
After that you'll want a brewing vessel. I started off and still adore my ForLife mug with tea infuser. It's a horrible mug for fancy, connoisseur type teas, but makes a wonderful, high volume container for cheaper day-to-day teas like Genmaicha, Houjicha, English Breakfast etc.
And, shh, don't tell anyone, but sometimes I make fancier teas in it too.
