I suppose both the historical and Shakespeare versions are conjecture but I would offer the following:
Historically - she was the love of his life having grown up together and been friends since childhood.
Shakespeare - she was joint heiress with her elder sister, of the Earl of Warwick - a powerful and rich man. Her sister married Richard's elder brother George, but when he was killed and attained that share of the fortune fell to Anne. She therefore was the richest woman in the land. Marrying her gave him financial power to back his own
Its ages since I read the play,but I thought that Richard was generally despised by people,Lady Anne included,and he won her round.He certainly never struck me as someone who could have any woman he wanted.