You have 3 possibilities, each with its advantages and disadvantages:
Improve cpu without modifying mobo. It is the most technically simple option. An intel of 6 or 7 generation is required. Unfortunately these cpu are overpriced for their power and so we have the I5-i5-7400 simpler costs about 160 eur. Remember update your BIOS.
Improve the cpu (with intel 8 generation). It involves buying a mobo of the 8 generation (chipset B360 or H310) and a CPU of the eighth generation.
The cheapest mobo can be Gigabyte H310M S2H Sockel 1151-v2 (65 eur) and CPU I3-8100 (106 eur). This option is somewhat more powerful than the previous one because the I3 of the 8 generation are similar to the i5 of the seventh (they have 4 cores) and have more frequency.
Improve your CPU by going to Ryzen. It involves buying a Ryzen compatible mobo (A320 or B350 chipset) and a Ryzen cpu. This solution has the disadvantage that Ryzen is very sensitive to the speed of the DDR4 memories. I suppose your DDR4 memories are 2133 (correct me if that is not the case). All the tests you will see on the internet are based on speeds of 3000 or 3200. This means that with your memory the Ryzen are 10% worse than what you can see in reviews. This is even greater in the Ryzen that have a built-in graphic card.
If you are not going to overclock, choose an A320 mobo. If you want to overclock choose a B350. For example the cheapest ones are:
B350 Gigabyte GA-AB350M-DS3H (65 eur).
A320 ASUS Prime A320M-K (60 eur).
How CPU can choose (order from highest to lowest)
Ryzen 5 1400 125 eur (without integrated graphics card)
Ryzen 3 1300x 112 eur (without integrated graphic card)
Ryzen 3 2200G 84 eur (virtually equal to the previous one and with integrated graphics card). It requires your vendor to update the BIOS of the mobo. You must find a seller who does it and should have a cost of about 20 eur.
These options are somewhat inferior to the I3-8100. If you could increase your budget you can get a Ryzen 5 1600 by 143 eur, much higher than all others we consider.
All prices are amazon.de (no shipping costs). They may differ slightly in other vendors. As you can see your budget is overwhelmed in all three cases.
So that we can advise you better, you should confirm the speed of your DDR4 memories and if you have a dedicated graphic card. If you do not know this data, you can obtain it with the CPU-Z program.