If RAM is cheaper then I'd go for a 2x4GB kit if possible. PCs will run faster with dual channel memory especially Ryzen.
I also recommend spending more an a quality power supply. You won't get one for 20 euro. It's the worst thing to cut costs on. Primary killer of gaming PCs is cheap PSU. Even if it means having to save up more.
I'd also consider spending to get an SSD as well if you don't have one.
i3 8100 is faster than i5 7400 but almost 10% slower than i5 7600 (which costs roughly €100 more). An i5 7600 would costs more to build though and the 7th generation Intel platform is already abandoned by Intel so all you could do with that motherboard is upgrade to a 7700k at best. But 7700k isn't a budget CPU. i3 8100 is the best budget Intel chips. The issue with Intel 8th generation is that the motherboards costs more. i3 8100 performs in games about as good as Ryzen 7 but as it has less cores and threads it's not as good for things like multitasking or streaming. Ryzen 7 costs way more though.
Based on your price range the 1300x is ideal. You could build a i3 8100 for more but it would only be like 5% better in gaming and you can't overclock the i3 8100.
Here's what I'd consider a good budget system for 2018 (without an SSD):
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 3 1300X 3.5GHz Quad-Core Processor (€118.66 @ Amazon France)
Motherboard: Asus - PRIME B350-PLUS ATX AM4 Motherboard (€81.66 @ Amazon France)
Memory: G.Skill - Ripjaws 4 series 8GB (2 x 4GB) DDR4-2400 Memory (€68.16 @ Amazon France)
Storage: Western Digital - Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive (€40.83 @ Amazon France)
Video Card: EVGA - GeForce GTX 1050 Ti 4GB ACX 2.0 Video Card (€193.90 @ LDLC)
Case: Thermaltake - Versa H22 ATX Mid Tower Case (€37.96 @ Amazon France)
Power Supply: SeaSonic - 520W 80+ Bronze Certified Fully-Modular ATX Power Supply (€54.90 @ Amazon France)
Total: €596.07
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-03-04 05:03 CET+0100
Prices vary by region. I'm using France for this build.