Make it woman tall and let the handle bend. Leave it 1.25 in wide out to mid limb. Choose straight grained stock or back with linen, burlap or silk. No knots. You don't need to back with wood...
I'll third all of that. I've built several red oak bows and none of them have blown up yet. You just have to make sure that the grain is nice and straight - AND tightly grained. Some of the Lowes Depot red oak has really widely spaced grain, and I've been told it makes weak bows. A fun option for a quick bow for a child is to use red oak quarter round - it's even already (half) rounded. I made a 5 pound bow for my 4 year old son that way, and backed it with linen for peace of mind.
You can get linen (and sometimes silk) dirt cheap from secondhand stores like Goodwill (old shirts and pants). I've been thinking of doing a denim-backed bow, but haven't heard if it is advisable or useful. I would think it would work great - it's very strong, and stretches a little, which could aid in tension. I've never tried burlap, but it sounds like it would work great. I've even using red oak to back a very weak non-bow wood (butternut) and it's holding up very well.
Don't try to dive straight in to using complicated (or expensive) woods - have fun making some stick and board bows, get a feel for it. Since I started, I've had four bows break on me, two during tillering, one was really bad (small cuts, whacked in the face, etc). But I've also made three successful, attractive, and fun bows. I'm finally working on my first 'stave' bow now, and it's coming out very well.
When in doubt, ask these guys for help! They're awesome, always have good advice, and never make you feel small for being 'new'.
