I didn't hire on at my Fortune 50 company in a job that required travel (on purpose, as I had teenagers at home) but of course it worked out that way. The single biggest argument we continually had is that I had to travel "on my own time."
No - you are requiring me to go to Texas or NY or San Francisco or Singapore for a meeting, so you can damn well pay me to do it. I'll leave Monday morning at 7 am, not Sunday at 7am.
Although we had a corporate travel site, airfare and hotel and car rental/taxi whatever had to be paid using the corporate-sponsored private AMEX card and then reimbursed, and of course the trip report never managed to get reimbursed before the payment was due, so frequently I was floating the company a $5K "loan". Helluva racket, that. I started flat-out refusing to go to Singapore when they started requiring that you make 3 international trips a year in coach before they'd upgrade to business (and FF miles belonged to them).