Laurie, what phone carrier do you use and what model of iPhone do you have?
I have an factory unlocked IPhone 5 that I use on T-Mobile, I've used four different SIM cards with no special settings required, just install the activated SIM card from whatever country I'm in and turn it on. (Data might need some special text to activate) All my settings, contacts, apps, etc. all stay the same. The iPhone also detects what country you are calling(no need for a special prefix) Plus I don't have to get familiar with a different phone, I find it a pain to text with a basic cellphone as most other do.
The only special item I need is a EU USB plug.
If possible, unlock the iPhone you already own and just swap SIM cards as you travel to each country.