I'm a huge fan of skirts, not much experience with dresses. And I am the opposite to you: late thirties and would love to feel good in slim fit jeans and tops with converse or flats! I keep trying to work on it but I am so weirdly shy of my ass in jeans (as far as I know there's nothing wrong with it really, but I can't shift the paranoia). I need some confidence!
But yes, perhaps try skirts like knee length full or aline, depending which suits your shape best, and occasionally pencil skirts, shorter with tights or knee length with a nice pair of mid heels or flats. I like to wear silk shirts loosely tucked in, or check shirts, blouses, etc. For a more casual look I can dress down a pencil skirt (avoid black if going for casual with pencils) by teaming it with a white tee and patent flats.
Places which seem to sell decent enough skirts for your requirements might include Hobbs (amazing quality skirts in my experience), Jaeger, Jigsaw, Reiss, occasionally Oasis and Warehouse. These stores will also provide similarly cut dresses at a decent length. Also check out House of Frazer online and John Lewis for a decent selection of brands.
I shall go and practice trying to wear my skinnies now! (must admit though my converse have been sitting unused since spring, due to the weather being too naff to wear them)