You know those 3M hooks that remove without leaving any damage to the wall? They have them like that only not hooks, but with velcro tabs. They are marketed as picture frame attachers. But I think you could use them without worrying that they would leave a residue on the carpet. You'd put some of them on the carpet and some of them on the runners, and then they snap together. You can separate the velcro tabs when you want to wash the runners. I don't think you'd have to remove them, but I'm not sure how the ones on the runners would do in the washing machine. You could always remove the velcro tabs by pulling the glue strip down and put fresh glue strips on the velcro strips on runners after washing. They are pretty cheap. They sell replacement glue strips separately so you could reuse the velcro parts.

I like the carpet that resembles sisal. It has some texture that adds some interest but it's still neutral. It also has a little color variation so spots don't stand out like a sore thumb. https://www.mohawkflooring.com/carpet/detail/4162-75895/Sisal-Impressions-Harvest

Work with your local mom and pop shop and not the big box stores. Talk to the salesperson about the benefits of polyester, nylon or wool then decide which option is best for your budget. Once you’ve gotten to that point then take sample boards home to decide what looks best with your existing paint/furniture/existing hard surfaces.

Pick your bedding first.