Welcome to the forum. This really is a great place for shoppers to learn and share.
As for your question, there are lots of shoppers who put their business expenses on one credit card. It's easier to keep those separate from your other finances for tax time.
Yes, the wise use of any credit card will help you build your credit. Realize the income & reimbursement may not come in as quickly as the payments are due. Check each company's payment schedule to see when they promise payment. Check the forum to see how well each company delivers on their promise. Don't worry too much, most do it as promised.
Have fun with it.
Happily shopping Rhode Island and nearby Massachusetts and Connecticut