The only problem with giving them Linux is a lack of support for some applications. For example, I had installed Arch on my livingroom PC for my family, and set it up so that the kids can just click on their picture to log in. My wife needed applications that are not well-supported by Wine, such as iTunes. I was able to find workarounds, but they weren't very elegant, and weren't things I could have my wife do. Taking iTunes as an example, I had to manually mount the volume, extract her pictures, and reset her photo roll. It became a very messy monthly project to have to do for her, and one of the reasons she would state she hates Linux. Also, she likes photo editing, and there wasn't an application/suite that she could find that she really liked and could edit easily. After 2 years, she finally won and we got Windows 8.1 for the family PC.
If the person you are trying to help doesn't have a preference for applications, and isn't set in their ways for a certain application, any distro with a good graphical package system should work. Mint is very good for beginners, as well as Ubuntu. If you need to meet lower system requirements, take a look at XFCE and LXDE alternatives.