I'm thinking about this as well. My mother uses Windows 7 with Firefox, Thunderbird for mail, LibreOffice and Windows Photo Gallery. I think Ubuntu LTS with the Unity desktop is the best choice. Mint is an option.
In my experience Fedora/Centos is much more work installing applications. That may be my lack of experience with using Centos for desktop. If it's only about the browser, it won't matter much, and then your experience is leading.
I have a Lenovo laptop with 2GB RAM and Ubuntu 14.04 installed on SSD. It stalls many times. You need 4GB RAM. It will work on that laptop, but with issues, probably the same issues she has now. Better buy a new cheap laptop and make sure it has at least 4GB RAM.
Be careful with UEFI - it can cause many headaches when you want to install Linux. It took me more than a month to get it working.
Last tip: Try to find a laptop that has a proven record to work with Linux. Not all laptops qualify, have a modified motherboard or graphics card etc. The old laptop can be tested with a live stick.