The best processor that motherboard can handle is going to be the Intel Core I7-3770K, though the I5-3570 processor would be a nice upgrade as well. If I'm reading your RAM correctly (2x4GB DDR3-1600), that's good enough for now.
An upgrade to a new lower-end Intel system would be possible (depending on location - I used Germany's PC Part Picker to use Euros):
PCPartPicker part list /
Price breakdown by merchant
CPU: Intel - Core i3-8100 3.6GHz Quad-Core Processor (€106.00 @ Amazon Deutschland)
Motherboard: Gigabyte - H310M S2H Micro ATX LGA1151 Motherboard (€63.99 @ Amazon Deutschland)
Memory: G.Skill - Ripjaws 4 series 8GB (2 x 4GB) DDR4-2400 Memory (€67.59 @ Amazon Deutschland)
Total: €237.58
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-07-27 14:35 CEST+0200
You could also go with a first gen Ryzen upgrade:
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 5 1400 3.2GHz Quad-Core Processor (€117.90 @ Caseking)
Motherboard: Asus - PRIME A320M-K Micro ATX AM4 Motherboard (€61.08 @ Amazon Deutschland)
Memory: G.Skill - Ripjaws 4 series 8GB (2 x 4GB) DDR4-2400 Memory (€67.59 @ Amazon Deutschland)
Total: €246.57
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-07-27 14:40 CEST+0200
Or, once the new B450 motherboards become available, a lower-end. 2nd Gen Ryzen:
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 3 2200G 3.5GHz Quad-Core Processor (€98.84 @ Mindfactory)
Memory: G.Skill - Ripjaws 4 series 8GB (2 x 4GB) DDR4-2400 Memory (€67.59 @ Amazon Deutschland)
Total: €166.43
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-07-27 14:41 CEST+0200
Personally, I'd stick with the better processor on your current setup.
-Wolf sends