Need new chainwheels for a cheap racing bike - which price range makes sense?
You probably foremost need a neww chain and you will also need a new cassette. 

What you are linking are chainsets. You can normally just buy new chainrings for your existing crankset. As others mention in the comments, check first, whether the aluminium thing we see in the photograph in the top-right corner is a bolt that can be released with a hex key or a rivet. If it is a rivet, you will need a whole new crankset. See the bottom of the answer for a new crankset.



First for the cassettes

You can buy any 8 speed cassette that fits your rear derailleur in terms of size of the cogs - sprockets. The current one is 12 - 25. You likely have the RD-32 derailleur with max cog 28T and total capacity 39T. That means you cane safely go to even to 11-28T cassette.

In general, 8 speed cassettes are pretty cheap but those with older sprocket sizes (like yours) tend to cost more. I do not know why, but I do see it n the shops. But you can look around for the best deal, they are intercompatible.

With a triple crankset you can keep your small range cassette 12-25 but you can think about a wider 11-28. You get a bigger range, but also bigger differences between gears and more overlap between chainrings. But as I wrote, for some reason they appear to be cheaper and easier to find. Like here https://www.bike-components.de/en/Shimano/Claris-CS-HG50-8-8-speed-Cassette-p35939/

But shop around, look for HG-40, HG-50, HG-200 or Suntour 8-speed cassettes and see if they also have a cheap 12-25 somewhere. I did see it on Czech eshops but they were more expensive.

Do not forget that firstly you need a new chain and measure the chain stretch regularly next time so you do not neet the buy the cassette next time. A new chain is much cheaper. A chain measurement tool (chain gauge) is worth the investment. Even in terms of money saved.



From the update it is clear you also need new chainrings:

Buy new chainrings, unless there is something really bad with your cranks that you did not show. But I regard this as unlikely. If the chainrings can be released by the hex key.

You probably have this crankset http://www.pro-wheel.com/main/?product=ounce-631-tt or a very similar older model. The linked one is 9-speed but you may have an 8-speed version that is no-longer advertised. In that case it is 130 mm BCD and 74 mm BCD. It is best to measure it yourself. Or, you would at least give us a better picture of the crankset. Best with some scale, like a tape measure. In the Decathlon link the BCD size is actually written on the 

You can also buy from other brands, not just ProWheel. You also can change the sizes. You have 50, 39 and 30T but that can be changed, if you keep the difference. If you are not experienced judging what is fine, I would keep 50, 39 and 30, though.

For example, something like this https://www.sjscycles.co.uk/chainrings/compact-chainring-steel-110mm-bcd-5-arm-silver-50t/  Just to give you a picture how it should look like. You have to shop around in your country.



If you want to buy a new crankset or even a combo with a chain and a cassette, remember that you need a triple one. Currently you have 50-39-30. You will often see 48-38-28. That should work too. It may require readjusting your front derailleur. 

With a new crankset you will probably need a new bottom bracket. They are sold with different length. You will have to find out the correct length for your new crankset. And, if you ugrade to something with a different bottom bracket type (like Octalink or even Hollowtech II) you need the correct type. The cheapest cranksets use all square taper bottom brackets but with different lengths.