It's more about how much you think you'll need rather than just copying recommendations.
250GB + 1TB makes sense if you need ~1TB, it doesn't if you only need 400GB. Same if you think 2TB might not be enough.
This is TF2, so more than 4 cores won't help.
You're not going to overclock or use SLI/XFire so you don't need a mobo that supports those.
PCPartPicker part list / Price breakdown by merchant
CPU: Intel - Core i3-8350K 4GHz Quad-Core Processor (€179.00 @ Paradigit)
CPU Cooler: be quiet! - Pure Rock Slim 35.1 CFM CPU Cooler (€29.95 @ Bytes At Work)
Motherboard: ASRock - B360M Pro4 Micro ATX LGA1151 Motherboard (€93.95 @ Bytes At Work)
Memory: G.Skill - Ripjaws V Series 8GB (2 x 4GB) DDR4-2666 Memory (€96.95 @ Bytes At Work)
Storage: Crucial - MX500 250GB 2.5" Solid State Drive (€71.95 @ Bytes At Work)
Storage: Seagate - Barracuda 2TB 3.5" 7200RPM Internal Hard Drive (€66.90 @ Paradigit)
Video Card: Gigabyte - GeForce GTX 1060 3GB 3GB Windforce OC Video Card (€265.95 @ Bytes At Work)
Case: NZXT - S340 (Black) ATX Mid Tower Case (€64.95 @ Paradigit)
Power Supply: SeaSonic - FOCUS Gold 450W 80+ Gold Certified Semi-Modular ATX Power Supply (€69.95 @ Paradigit)
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-07-11 15:55 CEST+0200
Didn't change the GPU yet, like I said you could get away with much less for TF2.
Cheaper, case just as an example.
PCP is awful for PSUs outside of the US so could find something cheaper.
The 8350K is purely for the clockrate, even though this means you'll need a cooler (-K CPUs don't come with a stock cooler), but you could get a cheaper cooler if you wanted to.
Basically your upgrade options are the 8600 (~6% compared to the 8350K) and the 8700(K) (~15%), which are disproportionately more expensive.
Obviously if you went with an 8350K, 8600K or 8700K anyway you could get a Z370 mobo and overclock, but like I said it's only worth it if you're actually going to do it. You'd get maybe 3-5% with the faster RAM that Z370 allows, but the RAM would also cost a lot more.
Essentially the question is how much are you willing to spend for an extra 10 to 20%. 100€? 200€? 300€?
As downgrade the G5600 would actually be an option. If TF2's behaviour hasn't changed significantly since I benchmarked it, the G5600 would actually be faster than the i3-8100. On pcp Belgium it's 105€ for some reason, should be ~90€. About 90-92% of the 8350K's performance at literally half the price isn't too bad.
With the G5500 as a placeholder to get a more accurate price, a cheaper GPU and potentially a cheaper PSU you could get it down to 700€. https://be.pcpartpicker.com/list/sfF2r6
The main problem is I've got no idea what settings you want to use and I've got no idea what it takes these days to get 200+ fps in TF2, especially since the requirements for 6v6 are vastly different from HL/pubs.