Upgrade

You need to know if the crashes are caused by hardware (e.g. overheating) or software (e.g. drivers) first.

Didn't even think to check the minimum spec!

I suppose OP could throw in an old budget GPU like a Radeon HD 7850 (28eur, 1x6-pin power), GTX 660 (40eur, 1x6-pin), etc.

Or if it's an old Dell-type office PC, try to fit a GTX 750 Ti (55 eur) which requires no additional power connector.

Any PCI-Express graphics card works as long as you can supply it with power (PSU).

I was going to say the same as K.O. Kiki about the 470 4GB and giving it a clean ;)

You could also get another 2*4GB of ram from CEX for €4 while you are at it. That's the sort of money I could live with putting into that machine.

No, it's DDR3 for your board. So https://ie.webuy.com/product-detail/?id=smem9qai is what I'd probably go with (1600Mhz, the fastest your board will like) but depending what speed ram is already in there it might make no difference to just get https://ie.webuy.com/product-detail?id=smem9qah (1333MHz) or even https://ie.webuy.com/product-detail?id=smem4qaab (1066MHz) if it makes it easier for you to get them. And tbh at that price if you have 1066MHz (lol or even 1333MHz) in there now just getting 4 sticks of 1600MHz for €8 is certainly an option.

Yes, if you put in a graphics card you will want to connect your monitor to the graphics card. Any of the graphics cards mentioned will have a hdmi port (or at least I don't think there's any bizarre cards out there which wouldn't).

Your second sentence got cut off or had a couple of extra words: "Will I need to do that and will"

I would be wary of buying RAM from CEX unless you have a local branch you can buy from/return something to that you bought online. They don't test RAM, the amount of wrongly labelled/faulty RAM I've gotten from them is pretty high.

Also, you already have 8GB, which is plenty for Factario. I would just get the new graphics card first and work from there.

This is probably the best value card they have at the moment. But it may be overkill for your needs, it's certainly total overkill for Factario. But it would allow you to play much more modern games than Factario well enough, in fact it's capable of running games the i5-3570 is not.

https://ie.webuy.com/product-detail?id=sgraradrx4704ga&categoryName=graphics-cards-pci-e&superCatName=computing&title=amd-radeon-rx-470-4gb&referredFrom=category&queryID=5957829612850dbdac6d814ec45d5dfb&position=24

If you just want to do it as cheap as possible rather than spend €85, this will do perfectly fine for €30 as well. I'd personally learn towards this one if it's really just Factario and similar games you are playing.

https://ie.webuy.com/product-detail?id=sgraati78502gb&categoryName=graphics-cards-pci-e&superCatName=computing&title=ati-radeon-pitcairn-hd-7850-2gb&referredFrom=category&queryID=5957829612850dbdac6d814ec45d5dfb&position=9

Also keep in mind you said initially that sometimes the PC freezes or crashes. This might indicate a problem with the PC - though it could just be bad graphics drivers not playing well with Factario.

Yes. Be sure that your new graphics card has an hdmi port. Make sure you know how to distinguish hdmi from dp: https://uk.pcmag.com/how-to/117669/hdmi-vs-displayport-which-should-i-use-for-my-pc-monitor

If I was talking about the €12/stick CEX want for 8GB sticks (let alone probably €45+ for 2*8GB for new sticks and worse value for 4GB sticks) I'd certainly understand thinking twice about it and worrying about getting bad ram from CEX. At €2/stick I wouldn't be sweating about the risk of bad CEX ram, especially if I could pick them up from somewhere (hence I'd said 1066 or 1333 if it was easier and getting 4x4 should make the worst cases nothing bad).

To quote myself "That's the sort of money I could live with putting into that machine."