Total: £954.05
(includes shipping: £13.20)






You could save even more money by re-using the PSU, although I assume it's a few years old now and thus out of warranty?
Could choose a cheaper case also.
The 8600k generally performs better in games at common resolutions (1080p), although it has 2 fewer physical cores which could limit streaming capabilities. You can overclock the 8600k to be ~1ghz higher than the 1700. The prices of the 8600k should drop by ~£20 in the coming weeks as stock levels stabilize. The 8600k will also need a £50+ air cooler or equivalent AIO water cooler to get decent overclocks.
The 1700 usually performs worse in games, but the extra cores will help with multitasking at the same time as gaming. The 1700 is usually the better CPU for heavy multi-tasking and productivity applications, such as video editing etc.
Of further use - AMD have confirmed that the AM4 motherboard platform will support future Ryzen processors until 2020 - this could be useful if you wanted to upgrade the CPU later on. Conversely, the Z370 will likely (not confirmed) support Intel's 9th gen of CPUs, so there is a potential upgrade path there as well.
I would say that the choice depends on just how much you intend to stream, and if you intend to keep the system 'whole' or possibly upgrade parts in the next 1-2 years.
If you wanted to reduce the upgrade cost even further (at the obvious expense of performance):
- Swap the i5-8600k for an i5-8400 and a cheaper Z370 motherboard
- Swap the Ryzen 1700 for a Ryzen 1600, and change from X370 motherboard to B350.