If you run cat7 into a cat5e patch panel, you will get cat5e performance, not the 10gb/s you are looking for. To get cat7 performance from your cat7 cable, you would need a cat7 patch panel, cat7 modules and cat7 RJ45 jacks. These are all harder to install than their cat5e equivalents.
Cat6a can maintain 10 Gbps over up to 100 meters but without the huge cost hike of cat7. As 50'≈15m, you are well within the distance limitation, but would be at the upper limit of the speed that copper - any copper - is capable of. Equally, you need to pair it with cat6a patch panels, modules and RJ45's to avoid bottlenecks.
As I understand it, your core requirement is fast transfer to your NAS, rather than being desperate to install cat7 for the fun of cable installation. As you need 10gb/s today, I would expect this to grow over time, and since 10gb/s is the upper limit of what copper is capable of you could quickly run out of capacity if you use copper. The speed of copper cable is limited by the fact that the cable is made of copper, whereas the speed of fibre optic cable is limited only by the kit that you connect to it - and you can upgrade that in the future much easier than you can install a new cable. Yes, Cat8 might technically be capable of 40Gbps, but that's it. When you buy a shiny new 100Gb/s network switch in the potentially near future, your copper will be useless but your fibre will keep on trucking. I should also note that 400gbps networks exist in data centres today (Cisco, Juniper), so we could see that in the consumer space in the next decade.
For high performance applications, you will not want to be limited to 10gb/s forever. For example, the Insta360 Titan can already do spherical video, often colloquially called "VR", in 11k. Insta360 have told me via email that one minute of footage can require up to 10.8 gigabytes of storage. On an ideal 1.25 gigabyte per second connection (1 gigabit = 0.125 gigabytes) it would take almost five minutes to transfer a 30 minute video file today. What about when the next thing is released that has even bigger files? With copper, you are already working on the upper limits and its stuck in your walls, so you will just have to suck up the time increase. With fibre, however, you would just upgrade your NIC & switches. The aforementioned 400 gigabit per second setup would transfer the same video file in about 6 seconds.
- Fibre optic cable is not vastly more expensive than Cat6a.
- Speeds can be bonkers fast.
- Distances can be bonkers long (kilometres).
- Electromagnetic interference is not a concern.
- No Power over Ethernet.
- Installation can be a pain - optical fibre is glass so ensure that you get a pullable product.
- Photonic kit is still more expensive.
- Cable termination is a pain.
- Not as widely adopted as copper in the consumer space - only your most nerdy friends will have a photonic/SFP+ NIC.
I would suggest running 4 Cat6a cables to each room in your house, alongside 2 fibre optic cables. This still allows you to use PoE, but also gives you the god-like transfer speeds where needed. For us in the more rainy side of the pond, four RJ45 euro modules also conveniently fills a double gang faceplate, though I appreciate that these might look a little unusual for all yall on the other side of said pond.
Regarding purchasing more cable than you need, never run one of anything.
- It will inevitably break leaving you with another job. While you have got the floorboards up, you might as well throw another cable or three in there; cable is cheap, ripping the carpet, floorboards, walls etc up again is expensive.
- In two years you will wish you had "just put one more port right there". This is why every room in my house has at least 4 Ethernet ports.
If you are putting one cable in, it takes about the same amount of effort to put 4 cables in, so you might as well put in 4. Additionally, it is always helpful to have spare cable in stock just in case.
I would strongly suggest dumping copper entirely for this application and going with optical fibre. It is the most cost effective and future proof option.