#2660
Well 250GB SSD + 1TB HDD costs almost the same as a 500GB SSD, so if 1TB is more than enough then maybe 500GB are enough and you don't need to worry about what to put where? Also you can just keep your old HDD.
Windows 8.1 I hope?
Not so much TF2 related problems with Win10, only Win10 related problems with Win10. E.g. replacing working drivers with broken ones, automatic updates, breaking full screen, breaking VSync, forcing VSync and so on.
Main problem with Win8.1 is actually that Microsoft decided since even after they announced there would be no performance updates for new CPUs on Win7/8 no one wanted Win10 it was time to take drastic measures and block all updates if you dare to use a new CPU with Win7/8. Of course there's a user-made patch that just disables the software they use for detecting offending CPUs.
The other problem would be Win8(.1) being weird in general, but most of that can be fixed with e.g. Classic Shell (except the control panel being split between metro and classic interface, only Win10 fixes that).
So here's a few options. These are by no means the final partlists because pcp is awful for Germany (outdated prices, few shops, counts shipping for every item so everything <100€ basically defaults to Amazon).
PCPartPicker part list / Price breakdown by merchant
CPU: Intel - Core i5-8400 2.8GHz 6-Core Processor (€239.99 @ ARLT)
Motherboard: ASRock - Z370M Pro4 Micro ATX LGA1151 Motherboard (€113.96 @ Mindfactory)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-2800 Memory (€183.76 @ Amazon Deutschland)
Storage: Samsung - 850 EVO-Series 250GB 2.5" Solid State Drive (€93.98 @ Amazon Deutschland)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive (€41.32 @ Amazon Deutschland)
Case: Cooler Master - N200 MicroATX Mini Tower Case (€40.46 @ Amazon Deutschland)
Power Supply: Corsair - CXM 550W 80+ Bronze Certified Semi-Modular ATX Power Supply (€73.13 @ Mindfactory)
Total: €786.60
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-22 20:19 CET+0100
Probably the fastest just for TF2, assuming it actually gets the full turbo clockrates (might have to fiddle with mobo settings because of power draw, maybe add a cooler because of the heat).
PCPartPicker part list / Price breakdown by merchant
CPU: AMD - Ryzen 5 1600X 3.6GHz 6-Core Processor (€209.00 @ Caseking)
CPU Cooler: CRYORIG - H7 49.0 CFM CPU Cooler (€34.90 @ Caseking)
Motherboard: Asus - PRIME B350M-A Micro ATX AM4 Motherboard (€76.99 @ Amazon Deutschland)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-2800 Memory (€183.76 @ Amazon Deutschland)
Storage: Samsung - 850 EVO-Series 250GB 2.5" Solid State Drive (€93.98 @ Amazon Deutschland)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive (€41.32 @ Amazon Deutschland)
Case: Cooler Master - N200 MicroATX Mini Tower Case (€40.46 @ Amazon Deutschland)
Power Supply: Corsair - CXM 550W 80+ Bronze Certified Semi-Modular ATX Power Supply (€73.13 @ Mindfactory)
Total: €753.54
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-22 20:20 CET+0100
Cheaper, better for streaming, but slightly worse for TF2 when not streaming.
If you were willing to overclock you could get the 1600 instead of the 1600X, would end up being the same speed. 15€ isn't much but you can actually get away with using the stock cooler (1600X doesn't include one) even with an overclock so it ends up being >=50€ cheaper.
PCPartPicker part list / Price breakdown by merchant
CPU: AMD - Ryzen 7 1700 3.0GHz 8-Core Processor (€284.59 @ Alza)
CPU Cooler: CRYORIG - H7 49.0 CFM CPU Cooler (€34.90 @ Caseking)
Motherboard: Asus - PRIME B350M-A Micro ATX AM4 Motherboard (€76.99 @ Amazon Deutschland)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-2800 Memory (€183.76 @ Amazon Deutschland)
Storage: Samsung - 850 EVO-Series 250GB 2.5" Solid State Drive (€93.98 @ Amazon Deutschland)
Storage: Seagate - BarraCuda 1TB 3.5" 7200RPM Internal Hard Drive (€41.32 @ Amazon Deutschland)
Case: Cooler Master - N200 MicroATX Mini Tower Case (€40.46 @ Amazon Deutschland)
Power Supply: Corsair - CXM 550W 80+ Bronze Certified Semi-Modular ATX Power Supply (€73.13 @ Mindfactory)
Total: €829.13
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2017-11-22 20:22 CET+0100
Even better for streaming, but probably overkill. Also basically requires an overclock or you'll get less fps in TF2 than with option 2 (with an OC it would be the same).
You can change your mind about SSD/HDD and overclocking or don't, then you can pick one of the three options and I'll make the final partlist.