A few years ago, roaming within Europe was quite expensive. Since then, the European Commission have identified roaming as a notable impediment to the single market, so have been taking some strong steps to remove roaming as a problem.
As of the 1st of July 2014, the maximum allowed roaming rates for an EU phone in another EU country have dropped again, and can now be no higher than
Outgoing voice calls (per minute) - €0.19
Incoming voice calls (per minute) - €0.05
Outgoing texts (per SMS message) - €0.06
Online (data download, per MB*) - €0.20
All of those are the maximum allowed, but before VAT in your home country. They may well end up falling again in coming years. You may end up paying less.
Most of the European mobile operators now offer plans which bring the cost of intra-European roaming down even more. Some even offer free roaming in some or all of the EU, it varies by operator.
One of the stated goals of the EU Commission is for there to be no roaming within the European Union, and have customers able to select a plan from any operator anywhere in the EU and use the phone anywhere else without extra charges. It's still some way off that, but things are changing for the better of the European consumer.
For now, you'll need to check the details of your plan and planned operator closely, and compare it to where you're likely to want to be using your phone. If the maximum roaming rates above seem fine to you, just pick whichever provider you want based on their domestic price plan. If you plan to travel quite a bit, give serious consideration to paying a little more for your base price plan, in order to get cheaper or free roaming within the EU.
(For the UK, in July 2014, you have one network who offers free roaming in many but not all EU countries + a few non-EU ones, several who offer to let you use your UK price plan in other EU countries for a small daily fee, and at least one who offers free EU roaming on their more expensive plans)
Exact plans / offerings / prices change pretty much from month to month, so you're likely to need to check the exact situation once you arrive.