I am also relatively new to tea. I'm a lifelong coffee drinker, and never would have guessed that I would enjoy tea. I didn't know what I was missing. I drink both green and black, but particularly enjoy black tea with milk and sugar. Earl Gray is a favorite currently.
I have been toying around with various methods for about a year. I have purchased a couple of teapots from Bodum, and have had the same frustrations you have experienced. Recently I hit upon a method that has worked tremendously well.
First, instead of a teapot I use a stainless steel (non-reactive)
2-quart sauce pan with a good-fitting lid. I bring the water to temperature (boiling for black tea). When it's ready, I take it off the heat, dump in the tea and pop on the lid. I then let it brew covered for the preferred time (normally 3-5 minutes). By the way, this works with both bagged tea and loose leaf.
In the meantime, I have microwaved 4-6 oz of water to boiling, and use it to warm up an insulated carafe -- in my case a Nissan (by Thermos) stainless steel carafe. I pour this into the carafe, put on the lid and let it warm up. If you don't do this you won't maintain the temp when you put the tea in.
When the tea is ready, I dump the water out of the carafe and pour in the tea. If I have used bagged tea, it's a simple matter of pulling them out. If it's loose leaf, I use a funnel fixed with a white paper coffee filter and pour the tea through it into the carafe. This captures both the tea leaves and fine sediment. If you don't like that a fine mesh strainer would also work. Pop on the lid and you have a carafe of steaming hot tea that will stay that way for several hours. The first time I tried this it was PERFECT. The last cup was as good as the first.
This is my everyday method of making tea. I know it is not as elegant as a formal teapot. I love the clear glass pots that show off the beautiful color of brewed tea. But for practical purposes this is a great, simple way for everyday tea drinking. I am planning on buying a pot and warmer combo (I've got my eye on the Jenaer Museum teapot with warmer) for special occasions, but for now this will do just fine. I wish I had figured it out long ago.
One note -- I reserve one of these carafes for coffee, and another for black tea. I have been using a teapot for my green for the time being. But it's probably a bad idea to use a single carafe for both, especially crossover between coffee and teas. I got my carafe on ebay for $17, less than half the retail price.
Try this, it really works well.