Hi amymarie_5 nice question.
Now, if you was my new girlfriend, & I'm your guy, I would obviously expect something for this time of year, just as I would expect to buy you a gift or two, its nice & its thoughtful but, I would not want you to overspend, & seem too keen as of yet, as this keenness with gifts now & then will be better after many months of dating, so, I would suggest something useful, & romantic, that you can both share & get involved in together, to bond your relationship even further, & I would love the gift from you to be, a DVD or two, of my favourite movie/film subjects, that we could both watch together, & as an added surprise, a beautiful bunch of flowers.
Just my thoughts for a new relationship gift idea have a nice Christmas.
All the best. Dale