The OP said his company can be expected to take more than a month to reimburse, so I agree that an advance is appropriate - why should an employee be required to pay late fees and interest?

To the OP, you should discuss all of this in advance. First step as several have said is to get an advance to cover the travel, hotel, car, and your daily per diem. This way you would only be on the hook for the extra taxes applied by the hotel and rental car companies.

If your company refuses the advance, then get an agreement that they will cover your interest and late fees.

If they refuse an advance AND refuse to cover interest and late fees, then you work for a jerk of a company. I wouldn't resign over this, but I would let them know how I feel.

To answer your question, I travel often for work so I have a company credit card.