Can I take another job that I just found if I have signed an employment contract with another employer that begins 3 months from now? Could I be sued?

Theoretically you can be sued if your prospective employer suffers forseeable damages from your breach of contract, but Job A has a legal obligation to attempt to mitigate its damages.  As a practical matter, if you tell Job A that you have reconsidered, Job A will probably, in the 3 months it has before your job was supposed to start, be able to find someone equally good to replace you for the same salary, so it is unlikely to suffer any damages.  In other words, as a practical matter it is unlikely that you will be sued, but you could be.  The chances of being sued increase depending on (a) how good you are at your job and how easily replaced; and (b) whether Job B is a competitor of Job A.