If they are asking YOU to put everything on your own CC, and not providing you with some sort of company card, I would start out small and make sure they are going to pay you in a reasonable amount of time. Find out what the limits are as well. If this is a consulting gig, and you are new with the company, don't go crazy until you establish when you are getting your money!

If it is going to take a few months to get reimbursed, you may look into an AMEX sign and travel account.

ChrisR