My advice is to be suspicious of unsolicited offers, and really really really do your homework about the company if you get such an offer. They could be legit, but many times they are either a scam or a warm body seeker (insurance sales and for that matter any sales jobs come to mind).

If you are required at any time to put up your own money, drop the whole thing.

But for the sake of argument, let's say the company IS legitimate. There is nothing wrong with specifically asking about their travel policy. A reasonable policy is that F or C is permitted for any trip over X hours, usually 8 or more. They may require that all bookings are made by their own travel secretary/department or they may let YOU do it within a given budget. They may require YOU to pay and then offer reimbursement, or they may issue you a company CC.

My own personal choice is that I avoid companies who require reimbursement or use of my own CC..it adds a layer of PITA that I would rather not deal with. Many FT'ers in such organizations complain that the reimbursement is slower than the CC cycle and they have to pay out of pocket while waiting for the reimbursement check. Others have issues with having paid only to have the company deny the reimbursement on some obscure policy grounds. Don't put your own credit record at risk. There was one poster on here who was in the hole for 5k to his own Amex while his employer dragged their feet, and his credit was impacted. I only work for companies that offer an inhouse corp. CC, and have turned offers down based on this.