The conjunctions you are most likely to come across are although, and, because, but, if, or, so, unless, when and while.
There is a traditionally held belief that it is wrong to begin a sentence with And or But. Perhaps some schools still maintain this rule, but no one has come up with a good reason for it. Obviously, if it is unnecessary, then it should be left out – but since the earliest times the best of writers have begun sentences with And and But, to their stylistic advantage. It is definitely a rule to be flouted. But judiciously.