Looking to upgrade PSU for hp 400 g1 SFF pc

Jan 26, 2019
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I’m pretty new to gaming and I want to upgrade my PSU to 350-400W if possible from the built-in 240W one. The one I have has the serial part number 722299-001. Can you please help figure out what PSU I could buy that would fit in the SFF case. I don’t really understand much about PSUs and I dont want to make a mistake of buying something that won’t fit or anything like that.

The reason I’m upgrading is to be able to handle a CPU upgrade of i5-4570 (from penthium g3220) so it could handle games like csgo and warface better with the current graphics card i have (gt 1030-crap i know but I cannot upgrade that just yet)

I’d really appreciate any help regarding this. Thank you.
 
Jan 26, 2019
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Thanks for the suggestion. While looking into PSUs, I came across the part with all the connectors and I'm just worried if the PSU would come with the connectors in the correct pins?
I have this motherboard here (http://h10032.www1.hp.com/ctg/Manual/c04033294 .. page 4)

What exactly types of pins or connectors should I be looking for, for this specific motherboard?