I think you'll find your SIM card can store some numbers but nothing else. You can normally choose where to save downloaded files, either to the main memory of the phone or to a storage card (such as a microSD card, which is entirely separate from the SIM card), or you can always move them manually.
Your data and files should just stay on the phone, either in main memory or the SD card (if you have one).
I think there is a broader issue that you may need to check - certainly in the UK some phones are 'locked' to the network provider who supplied it, so check with them before you go to see if it will accept other SIMs. Alternatively you could just keep the SIM you already have and check out what the cost will be - roaming charges are greatly reduced these datas - just watch what they will charge for data... some people runs up bills of ££££s without realising.