Hi.
If you build a PC based around an i5 and an SSD, I suspect it will still be powerful enough for your needs in 10 years time.
You don't need to worry about a separate graphics card unless you are doing a lot of picture editing, video rendering or gaming. ( - see later remarks)
Quiet cases tend to be quiet expensive and unless you are building a thread ripper, possibly not worth the expense.
I wouldn't recommend AMD. Especially if you want a quiet machine. Some of the zen+ Ryzens are't proving unstable with default balanced power usage configurations that most motherboards and Windows use by default.
This would be my budget recommendation for a quiet PC:
https://uk.pcpartpicker.com/list/dp6BjyI've opted for a 250GB SSD - that should be ample for a Windows install and quite a number of applications
1TB HDD for storing your music, video and photos as it's more storage at less cost.
Switching out the 250GB SSD and 1TB HDD for a 500GB SSD would work out a hair more expensive. And although it would ensure you don't chattering hard drive to contend with (when it's spun up), overall it amounts to less storage for your buck. You could dampen much of the chatter from the HDD by literally suspending it on some elastic in that cases 5 1/4" optical drive bay. Unless you want to add a DVD/Blu-ray, in which case a different case might be preferable.
I haven't included a DVD/Blu-ray drive - probably an oversight on my part as I very seldomly use mine. In fact, in my desktop they are unplugged as to reduce it's energy consumption.
The i5-7500 has 65W TDP which isn't too shabby power/performance wise. You could switch it out for a 35W TDP i5-7500T which is underclocked. I doubt you would notice the difference in performance and it may make the PC run cooler and thus quieter. But it will set you back an extra £60. I would probably pony up for it if I was building the machine for myself, in my drive for an energy efficient household.
The case is very much a budget item. For the money they are excellent value and although they feel a bit flimsy, there aren't any sharp edges or massive impracticalities when assembling. I've built 40 or so PCs using the same case. It will seat 3 120mm RPM fans (more slow spinning fans is better if you want a quiet build). Remove the included fan and put it in the spares box, as it will be noisier and less long-lived then the Noctuas.
The fan configuration in the case is 2 inlet and 1 exhaust, which will make for positive air pressure in the case. This is good for keeping the dust down (negative pressure tends to draw more dust in) but is (slightly) less efficient. When the machine is under load, the PSU fan will spin up and probably bring the pressure down a little bit. You may want to opt for an alternative case that supports 4 fans (again, more slow fans = better for a cool/quiet build). That will bump the cost up slightly and, depending on the extremes of ambient temperature/workload on the machine, could prove to be unnecessary. If you want to err on the side of caution and try a different case/additional fan, let me know and I'll make a recommendation.
The Noctua CPU cooler and fans will make the PC whisper quiet. In fact, I originally built my server(s) with a similar cooling setup (before they were re-built into a rack cases and re-located to the garage) and the only thing that was just audilbe was the PSU fan when I'd got all of the hard disk drives spun up. When I rebuilt the servers into their rack cases, I had to switch the fans out and I've kept them ready for the day I build a silent desktop (which I can't afford/justify it yet).
You may want to add a passively cooled graphics card but:
(1) It will generate heat and the fans will have to work harder to expel it
(2) Some of the low-end/cheaper ones are no better than the on-chip Intel GPUs
(3) If you find you need one, you can always add it later
If you want to connect the PC via Wi-Fi, there is a variation of the selected Gigabyte motherboard with an integrated Wi-Fi adapter. Or you can add a PCI-E Wi-Fi adapter for not much.
In terms of longevity, my i7-3770 is now 6 years old and now I'm not running batches of 12-24 photos through sets of photoshop actions, still absolutely urinates over everything I throw at it.
I hope this helps. If you want to make changes, I'll more than happily to take your feedback and put an alternative list together for you.