Personally, for a first self-bow, I don't think you can go wrong making a red oak board bow.
The boards are about $7 at Home Depot so if you screw it up or come in under weight (common for a first bow), big deal. Make another one.
This is also a good way to learn the all important tillering process. Skills you gain making a board bow will be used later if/when you make a stave bow.
The Traditional Bowyer's Bible books are excellent references for bow making. Poor Folk Bows is great, and George Tsoukalis (sorry if I spelled that wrong) here on TG has a great little web site that will help you.
And yes, a red oak board bow can be hunted with.
Guy