Geez. There are only about a million website design companies out there.
Some companies only want to host the site. Some companies only want to design it for you, collect the cash, and then disappear. Some companies want to take the overall management of the entire website for a long period.
You have to decide what you need done.
Some years ago, I worked for a manufacturing company that had no website. I told management that we needed a website. Customers told us that we needed a website. Other vendors told us the same thing. I kept reminding management.
Finally, one day management came to me and said, "Bob, we've decided we want a website. What do we need to do?"
They wanted to appoint a task force to draw up specifications, then show that to various designers, then look for a host company, etc. They wanted me to scan product photos. Then they wanted me to head the task force. <b.s.>
Instead, I just built the whole damned thing myself. I bought the software, laid out the pages, collected the product photos, and tested it locally. Then I found a hosting company, uploaded the files, and away we went. It's really not a big deal.
---Bob Gross---