You need DDR3L-1866 (also known as PC3-14900).
DDR3L is low power ddr3 memory, basic memory will do perfectly fine in such a system. You don't need fancy brand, rgb or heat spreaders. Get two 8gig sticks and call it done, this is all your system can handle.
Beyond ram, I wouldn't put any more money into this box, the cpu is good, but it's showing it's age and the form factor really limits your upgrade path.
Now I have 2x4GB KINGSTON HYPERX GENESIS 1600 RAM, and I now ordered 2x4GB of the same RAM so I will have 16GB of GENESIS RAM.
(By the way-Unfortunatelly I cannot setup XMP in BIOS of OEM computer, do you know some other way or some software with which I could
turn on XMP and have all 4 slots of RAM in DC DUAL CHANNEL? XMP could make couple of percent improvement?)
Basically you are saying there isn't much difference, and the RFARMER responded here that 1600 MHZ DDR3 RAM could be best on my motherboard,
althought on his link I see CRUCIAL has 1866 RAM made optimal for HP800G1 tower (I have SFF, but it does not matter).
Even if I put on motherboard DDR3L-1866 RAM (also known as PC3-14900), there wouldn't be much difference than 1600, right?
It wouldn't be more about 5% faster in games, right?
Yes exactly, good point, I was thinking the same even before I posted to this FORUM - this box is limited,
when I saw I couldn't upgrade GPU much, I got an idea I could get in faster RAM and put GENESIS RAM out of HP800.
(best would be GT 1030 Low profile 35W GPU, right? And even this needs 300W PSU, I have 240W only,
plus benchmark is only 3 times better than integrated HD 4600 GPU,
which wouldn't make much difference for about 5 year old games and Android EMULATOR, right?
I do not need 1080p or stuff like that though, HOWEVER I was also thinking to try ANDROID and iOS emulators for games,
which seem very demanding for specs).
Another option would be to change the HP PSU for 320W HP PSU, I do not know is the correct model, but If
I found a good offer with good price for used one, that might be better than buying and setting everything on new computer, right?
Then I could put in some 75W LOW PROFILE GPU like GTX 1050TI Low profile or similar, although they seem more expensive
in LP version, which makes it even more expensive as I would already use money for 320 HP PSU and possibly shipping
(it would then be better to save that money for another computer or a game console).
Probably smartest would be to buy 2x8GB GENESIS DDR3 1600 RAM, so that I would then have 24GB RAM, right?
In the future I could even buy more and have 4x8GB GENESIS 1600RAM=32 GB
(and use 4GB GENESIS RAMS in another computer, it's good that RAMs are so 'transferable' and I wouln't lose money on it,
as I would on PSU and GPU upgrade).