Which Linux distro would work well on my 14-year-old laptop?

The NVIDIA GT 635M is old enough that its proprietary driver support is awkward on current kernels. Nouveau may work, but it can use more CPU, reduce battery life, and provide poor performance for demanding graphics. You could spend a lot of time trying to keep an outdated driver working, so I’d recommend using the Intel GPU and a lightweight desktop instead.

Linux should handle the Blu-ray drive itself, but playing commercial Blu-ray movies is a separate issue because many discs use copy protection. Reading files from an unprotected disc should be straightforward, while protected movies may require additional software and the necessary decryption keys. It’s worth checking that part specifically before choosing a distribution.

For your use case, I’d avoid relying on the old NVIDIA graphics chip. If the laptop has Intel integrated graphics, disable the NVIDIA GPU or let the system use the Intel graphics instead. That should make installation and everyday use much easier. A Debian- or Ubuntu-based distribution with the XFCE desktop, such as Linux Mint XFCE or MX Linux XFCE, would be a sensible choice for this hardware.

Your processor and 8 GB of RAM are still adequate for light use. The small SSD is the bigger limitation, so choose a reasonably lightweight installation and avoid filling the drive completely. XFCE is a good fit, and you can test a live USB first to check Wi-Fi, sound, graphics, and the optical drive before installing anything.