I'm not a woman who likes to receive flowers, but when I receive them by surprise, for whatever reason, I find it a very touching and thoughtful gesture on the part of the sender, so by all means go ahead and send her some. I don't know about sending them to work, though, unless you know that her colleagues are aware of relationship, such that it is at the moment. It could embarrass her. Home would be better.
Whilst lillies are nice, some people see them as being related to funeral stuff, especially the white ones, and they could give out a misconstrued message.
Gardenia are lovely, showy blooms that say 'you're lovely'. There are lots of others (including the tried and tested rose, of course), and if you Google 'language of flowers' you'll find plenty of websites that tell you what the different messages are. Here's one:
http://www.pioneerthinking.com/flowerlanguage. html
If she happens to understand the meanings of flowers, then send her the right ones and she'll be yours.