That is a nice set-up for only four hens, very nice.
I'm not sure what you mean by better. To me if the coop/run do not stink, are low maintenance, and the run does not stay a muddy mess after a rain or snow, well how does it get better? A lot of that in the run depends on how well it drains. If it is sand it may drain away pretty fast. Or if the run is raised so water drains away from it instead of to it you are usually in good shape. If water stands in the run you will almost certainly have issues. Part of it, coop and run, is your cleanliness standards. Some people are willing to work hard chasing every bit of poop while others are more relaxed about that.
In the coop the purpose of bedding is to act as a diaper. Bedding absorbs moisture and dries out the poop. Dry poop doesn't stink, wet poop will if it stays wet. Some people turn the inside of their coop into a compost pile, that's called the deep liter method. If it gets and stays wet it will stink, if it is too dry the microbes that turn it into compost cant live and reproduce, they need a little moisture. The amount of moisture needs to be low enough so that those microbes can breathe air. If it is too wet for the microbes to breathe air you get the wrong kind of microbes and they stink. My coop stays too dry for those microbes to live so for me it's just deep bedding, no composting action.
Whether or not you have droppings boards makes a difference. Poop builds up under the roosts because they are not moving around at night. If you manage that poop the rest of it builds up slowly so you don't have to clean it out as often. Some people clean the bedding out on a weekly or monthly schedule. Some clean it out once or twice a year. I clean mine out once every three or four years, but I put the poop from the droppings boards in my compost pile regularly so it does not build up in the coop. There are so many different ways you can manage the poop.
To me the run is different because rain and snow will blow in from the side. It's not a case of keeping it dry as letting it dry out after it gets wet. Good drainage really helps with that but if the weather sets in wet for a spell you can still have challenges. Deep litter works really well in the run for many people, for others not so much.
To me a good bedding should be readily available and reasonable inexpensive. It should be easy to handle, whatever your handling methods and how often you handle it. Some of the standards are wood shavings, wood chips, hay, straw, sand, dirt, dried leaves, or dried or green grass clippings. We all have our favorites but the reality is that different people successfully use different things. What works great for some of us is a mess for others. We are all unique in many ways.
My main suggestion is to try something and see how it goes. Be flexible. If you run into issues get back on here with what those issues are. It may not be your bedding, it may be a drainage problem.
That is a nice coop and run for four hens. As long as the coop or run does not stay wet for long periods I don't think you will have many issues. To me that's a good reason to give them plenty of room instead of shoehorning as many as you can into a tiny space. It just makes life so much easier.