I would definitely make my own travel arrangements so I can make sure they accommodate my needs (equipment/baggage, preferences, etc). Airlines have difference restrictions, some are more forgiving in some areas, and knowing this can help make the travel smoother. When the reservations are made, sometimes the person making them need to change a little detail or two, and if they aren't familiar with what the photographer needs it could turn a routine trip it a hassle. So I always do the reservations myself.
Also, expenses should be covered up front. This gets more and more important as the projects get bigger and more complicated, so why not start off right. It's not that big of a deal to front the cash for a trip on a smaller job, but when the travel expenses start to grow, you don't want a precedent set that has the photographer footing the bill.
I do mostly commercial work, but this applies equally as well to a destination wedding. I ask for 100% of the expenses to be covered up front, and don't start any job until I have that (plus a signed contract, Purchase Order, etc). In the instances that I forgo the advance, I charge a markup on all expenses. Since I'll basically be their banker, billing department, and have the risk that if they flake on me I am out the expenses, the markup is justified. Whichever way they choose, I'm ok with it since I'm covered with either an advance, or and additional 20% for the risk and effort.