Gone are the days when we had to use payphones to call home while travelling. Today, there is really no reason to lose connectivity while travelling. Of course, this does not mean that we pay hefty phone bills by using international roaming facilities. There are better options!
What you ideally need while travelling is a phone that has a local number and can make and receive international calls and texts. The phone can be any phone you like, and if you want, you should be able to add a data service to your contract.
What you essentially need while travelling is a sim only contract which allows you to use your own handset and get a local sim. There are cheap sim only contracts which can be perfect for maintaining connectivity while keeping your holiday budget down.
Depending on the kind of trip you're going on, you can choose a handset. For example, if you're going hiking through the Amazon valley, it is wise to carry a simple and sturdy handset. Although chances are that connectivity will be an issue in the forest, irrespective of how fancy the phone is.
For regular travellers, it makes sense to have a spare phone with a local sim. This can be used whenever you're abroad. There are different types of contracts, and you can choose one that suits you best.