Thank you very much. It is custom built on Wordpress based on the detailed scope I provided. Still lots of kinks to take care of, but the site is functioning and even selling names.
I prefer to do all my projects on Wordpress. I have been developing sites since 1999 and have learned the hard way that custom scripts can become headaches and relying on third party solutions can end up bad as your business is fully dependent on someone else.
Wordpress ecommerce or any ecommerce platforms from shopify to square are not build for domain trading. This is truly unique product that doesn't fit any category and has so many nuances. It is a virtual product, but not something downloadable, each product is unique. It doesn't have product brands, instead it has possible uses, feels, lengths, ages etc. So some customization is required.
Wordpress is not by any means a smooth solution. If you don't know what you are doing, you will end up with slow site that is easily hackable. But once you learn your way, it is a great tool. Some quick tips: always delete the default themes that you are not using, keeping just one and making sure it is updated; install only the plugins you really need and keep them updated; make backups; install wp cerber for security, use wp fastest cache plugin, use cloudflare (even the free option is good).
I rent a dedicated server, as I have other web projects too and it makes sense for me to have a machine that costs me $300/month, but for your needs a good hosting should be adequate. I also have a server admin I pay fixed monthly fee that takes care of server side issues. If you go wordpress route, make sure you have a wordpress expert that is readily available to fix any potential issues. Learning basics is certainly easy there.