If you haven’t done any gluten-free baking before, your best bet is definitely to find a GF baking mix – actually baking GF from scratch requires quite a bit of experimentation to get your recipes to come out the way you want them to. If you have a Trader Joe’s or a Whole Foods near you, both of them have very good GF brownie mixes – for some reason, it’s easier to adapt brownies to GF flour than cookies – the texture just comes out better. Betty Crocker also just started making GF mixes, which you can find at almost any grocery store at this point – I’ve tried the yellow cake, which is quite good, and I’ve heard the brownies are tasty too.
If you really do want to try something from scratch, I’d suggest buying a bag of Bob’s Red Mill GF flour and a bag of xanthan gum (Bob’s Red Mill makes that too), and making something that doesn’t count on flour for most of its substance (I’ve had very good luck with things like carrot cake and muffins, pumpkin bread and zucchini bread, since the veggies are what keep them moist and maintain their texture). Just use the GF flour, and add about ½ tsp. of xanthan gum per cup of flour (that gives it the stretchiness that you ordinarily get from gluten in regular flour). Good luck!