There are basically three smart phone operating systems: IOS, which is exclusive to Apple iPhones, Android, which is used by most other manufacturers, and Windows, which is only on a few.
IOS ties you into Apple but is very good if you don't mind that. iPhones tend to be a bit more expensive than an equivalent Android phone. Another "advantage" of IOS is that every time Apple issue a new version your phone tends to automatically update to it. Many Android phone stay at whatever revision was installed at purchase or sometimes are sold with a one-off upgrade to the next version that gets issued. iPhones also tend to have a bit of a bad reputation for battery life.
You have less choice with IOS. If you take the latest iPhone 6S as an example you can get versions with different amounts of storage varying from about €800 to €1,000 without contract from Vodafone in Greece. They also have 4 earlier models available from about €350 to almost €700. If you then look at Android there are 37 models available from about €60 up to almost €800.
Some Android phones are available in dual SIM versions so you can have a Greek SIM and a UK SIM if that is any use to you. I find it quite useful. They seem to be quite hard to find in Greece but I have bought from Mobicity
in the UK by mail order with no problems.
Some Android phones allow you install extra storage. It is usually cheaper to buy such a phone with small storage and then buy a memory card to extend it rather than buying the model with the bigger memory to start with. For example a phone with 128 GB of storage memory might cost €200 more than the same model with 16 GB but you can buy a top quality 128 GB micro SDXC card for less than €50.
Dual SIM and phones with a memory card slot often have an easily removable back so it is also simple to change the battery. You can often get a separate charger and carry a spare fully charged battery with you to give you double the battery life if you are going to be using it a lot away from a charging point.
Transferring photos shouldn't be a problem but check on a model you are interested in before buying it. Android isn't a completely uniform operating system. Many manufacturers customise it so what features are available can vary. Some phones are very close to the original Android OS while others are heavily customised. Samsung for example has a free Windows program called Kies that interacts with the phone when it is connected to the PC with a USB cable and allows you to transfer stuff in both directions and synchronise things like diaries and contact lists between devices. Some phones will simply appear as an external disk drive when connected to a PC so you can use Windows explorer to move files across.
If you find a model you fancy you might find a review of it on Expert Reviews
or you could read reviews on there first to decide which models to consider.
I quoted SIM free non-contract prices above. Phones are usually cheaper if you buy them on a contract or as a pay as you go deal but beware, often they are then locked to that provider. Also make sure you negotiate a new contract as soon as the original one expires. Obviously that contract is inflated so they recoup whatever they subsidised the phone for. If you keep paying at that price you are paying well over the odds. Finally choosing a previous model from the latest one will be cheaper.