Firstly, check out that shit up there... Get yo'self a free book.
Secondly, giveaways are a fantastic marketing tool. I already give away crap tons of digital copies of my books, it costs me nothing but the hours of labor and the $$ spent on art/editing. I highly recommend you give that shit away for free, often.
When it comes to physical copies, it starts getting more expensive to ship them to you, and then to the customer (unless you're not going to sign them, then it's a bit cheaper). I still recommend you use some of your budget to do this. Especially seek out giveaways run by other blogs with nice followings, you'll reach a (typically) engaged and dedicated audience.
I don't really have much else to say about that. I always add a personal note to the books I sign for giveaways, thanking the reader for taking the time and having an interest. That will usually net you a review in one of five different places.
Anyway, good luck to everyone entering ^_^ night kiddies.