As far as your project goes, a simple cross half lap of your frames at the intersections would easily suffice. As far as hanging them without noticable hardware, for a beginner like yourself, a French cleat would probably be the most simple way, but the boards you're using are quite narrow. Maybe try routing out a small and shallow mortise and use little slotted plates for the screw head to hang on. Thin boards with hidden hardware doesnt leave a whole lot of options for you.
Nothing in life that is "worth the effort" is ever easy.
Last edited by BigJim; 01-11-2019 at 08:43 PM.