Most of the security holes that get found affect servers rather than home computers, particularly if you have a good router, but it can be very frustrating to use a dead distro with a declining user base to seek help from.
It depends on how small your system is. You can run AntiX and Vector Light, complete with GUI, in just 64MB. Anything less than that and you're probably down to command line only. SliTaz would need more memory. Tiny Core is more of a kit for putting your own system together, unlike a conventional distro where you can just install and go.