I think choosing which LMB book to hook someone with depends on the interests of that person. My mum loves hard SF, so I gave her Falling Free. A friend of mine likes romances, so I gave her the Cordelia's Honor omnibus. Another friend of mine likes realistic medieval stuff, so I gave her the first of the Chalion books.
I call this campaign "Give a Bujold for a Birthday". Feel free to join in