With a little experimentation, I am sure you will quickly become able to make up better tea at home than is available in a bottle.
Which tea you use to start is up to you. Even the cheapest black teas usually make good iced tea, but I love using loose black teas.
For sweetening, just use regular sugar, or if you want to go fancy, try using honey. Start with a little bit, measure the amount you are adding per unit of water (it's usually easiest to make a pitcher and figure out how much to add to the whole pitcher), and then figure out exactly how much you like.
For adding lemon, you can add actual lemon juice (which I think often tastes better)...but if you want the tea to be lemony without being sour, you can instead grate up lemon peel and brew this in with the tea leaves...this will make the tea lemony without making it sour. Another option is to use a tea blended with lemon (like green tea with lemon, black tea with lemon, etc.), or to mix in a teabag of a lemon herbal tea when you brew the black tea.
Experiment! You will quickly find that you're able to make much better tea at home.