Exciting project, good luck with it! I live in the SW Chicago burbs and built a 10x12 shed from scratch a few years ago. The inspector in our county (Will) said more than 100sqft requires concrete slab, less can be wood or concrete. It's a floating slab, 4-6" thick with about 2" of gravel below it tamped down. I pounded in about (8) 1/2" x 4' rebar vertically in the ground ~3.75' thinking that would help, tied to the horizontal rebar. It probably didn't but made me feel good

I had 2.5 yards delivered for ~$320 from Ozinga (the first yard is the most expensive as that includes the truck cost too). The driver was patient with us as my brother was driving a borrowed bobcat. I overbought 1/2 yard as I didn't want to run short, so I framed up a garbage can pad which I was able to fill also.
For 5' x 15', delivered or bags - it all depends on the price. I just bought a few for a mailbox post and they were ~$3.50. So $160ish + mixer rental should be compared to 1 cubic yard delivered, and any wheel barrow rentals you'd need. I don't see hardly any concrete trucks on the road in our area compared to the last 5 years, so I'd imagine they are looking for business and would deliver a smaller load.
If you do go with the bags, shop around and pricematch. I would find the cheapest 80lb quikcrete bags and pricematch it to your favorite bigbox store. Last year I built a fence and needed (80) 80lb bags of concrete for the fence post holes. Menards had it on sale, so I pricematched it to Lowes and got an extra 10% off. Lowes delivered it on pallets wherever I wanted it. I mixed these by hand over 3 days in a wheel barrow. But for a shed slab, you could have them drop the skid next to the slab and rent the mixer and have it hopefully done in several hours with some friends.
If you do use concrete instead of blocks or wood, don't forget to get the moisture barrier padding to go between the concrete and the bottom of your wall, and use treated lumber for the bottom of your walls. Also, decide if you're going to put J anchors in the concrete when it's wet, or put in something like redhead anchors after the fact. I put J's in mine, and used redheads in several of my friends' sheds lateron, and I like the redheads afterwards. Much easier to line up between the studs and center after the fact when you are putting up the walls and squaring it all up.
Good luck with it!