Here is a link to some excellent recipes that are gluten free. She has vanilla cupcakes but, no plain vanilla cake recipes...I am thinking though that perhaps you could re work the Frosted Orange Creme Cupcakes....that particular recipe is Gluten Free, rice free and vegan to boot. You may find some other recipes on her site you can use..I know you said you lived in a rural area and didn`t have a lot of unusual ingredients...so, it is difficult for me to suggest alternatives not knowing what you have in your pantry. Karina is one of my go to sites for many many of the recipes I love to chow down on. http://glutenfreegoddess.blogspot.ca/2009/04/orange-creme-cupcakes-vegan-and-gluten.html
Another site is Baking Beauties...love many of her recipes as well....without these two I would have starved long ago...LOL. Anyhow this recipe doesn`t look too bad....I would sub out the milk with soy milk or almond milk and perhaps leave out the lemon and use vanilla and/or almond extracts.. http://www.thebakingbeauties.com/2010/03/gluten-free-layered-lemon-cake-with-lemon-whipped-cream-frosting.html.
Both these ladies live gluten free so they`ve played with the recipes until it works for them...Good luck