The Thompson Family

I don't know whether you can help me or suggest the best places to look for more information please. I'm afraid I don't have a lot to go on. My great-great grandfather Michael Frederick Thompson was born around 1836 and his sister Ann about 1839 in County Mayo. Their parents were John and Mary. John was a stonemason. Mary, Michael and Ann were living in Liverpool by 1851. Any help or advice you can give me would be very much appreciated.

Alison