Then should not, in general, start sentences very frequently. It's often a sign of 'stream of consciousness' writing, where you're writing down as you think, instead of writing with proper form.
'First, he went to the store and bought some eggs. Then, he came home and made cookies with the eggs. And on top of that, he built a gingerbread house.'
That's basically writing down what you think about the process, right? 'Then' in the above sentence is technically acceptable, but it's pretty darned boring. You can use more interesting constructions to write the sentence, that increase the description of the surroundings.
Try:
'The baking process began when he went to the store and bought some eggs. After he checked out and loaded the eggs in the trunk, he drove home and made cookies with the eggs. Once the cookies came out of the oven, he used the remaining eggs, along with some graham flour that he found in the cupboard, to build a gingerbread house. '
Still not amazing writing, but it does draw the reader in more with detail. It's not a bad idea to use 'Then' when you're just chugging out words, but when you go back and edit, one good pass is to replace meaningless flow-directors like 'First' and 'Then' etc. with more meaningful descriptions that flush out the surrounding details.
And really shouldn't start sentences at all, IMO; 'and' should appear in between two related concepts/thoughts, and should usually be used after a comma, not a period. Use a more interesting word to start sentences that you create from splitting runon sentences at 'and' points.
If you really want to know, though, go back and read from start to finish one of your favorite authors [one that's highly successful and published by a major publisher, and writes in the same general style as you - ie, unless you're trying to write in slang, don't use an author whose books are written in slang]. How often does Mercedes Lackey start a sentence with 'And' or 'Then'? I don't have an electronic copy to run a wordcounter on, but I doubt it's all that frequently.