From what I heard from my friend with a billingual kid (father is Polish mother is not): they've been using both languages from the beginning (even before the baby started to speak), the child mixes them at the beginning (using some words from one language and other words from the other language, often also creates new words mixing the rules of both languages), it just comes with time that the kid starts to "feel" the difference and separate the languages as two different ones, but you shouldn't be worried about it.
So I'd go with your option 1.
1) Could I just speak to her in Polish often enough that she'll understand what I'm saying sooner or later
Don't worry if she replies in English, be patient, a 3 y.o. kid can't grasp the concept of the future usefullness of knowing foreign languages, so you can't exercise any pressure on her, because it may cause the reverse reaction (she could reject this second "useless" language).
I think books in Polish would be too difficult for her as she's only a beginner, some songs (especially songs for kids) would be better for now - and it would be wise that first you familiarize her (through talks or games) with some of the words that are sung, so when she hears the song for the first time some words/sentences will be known to her, this way she might be more interested in learning what the whole song is about.
Generally for a kid that already speaks one language (English in this case) you have to be more resourceful, the kid must feel that this new language is usefull to her/him too. There must be some kind of a "reward" attached.
Kids living in a mixed environment, playing with other kids of different nationalities will start learning without a problem, because they will need those new "strange" words for an activity they love. So you should play with her using gradually more and more Polish.
And I'm also sure that if you say to her several times "chcesz cukierka" instead of "do you want a candy" (or some similar "rewarding" questions - if you don't want to feed her too much sweets :) she'll remember it. Maybe some Polish cartoons could be usefull too.
So generally, you should use Polish when she has "some interest" in understanding (activities, things she likes).