While 500W psu is not great, for a RX 580 + an entry level CPU it may be enough, if the psu is really good and from a well known brand.
In any case Lutfij is right, and you should really be carefull not to use any generic and false advertised wattage PSU.
Whats your PSU brand and model?, 500W alone is just not enough.
Ok now to the CPU question. Hoping that your 16GB DDR4 3600 Mhz memory, are in fact 2x8GB DDR4 3600 MHz sticks, you wont be able to use them at that rated "speed" with that Core i3 9100F. Not unless you get an overclokable motherboard (which does not make much sense, specially since we are talking about a dead platform - 10th gen intel CPU are here... well some of them... when you can find them in stock).
Now if you need to keep the budget low, and have the correct RAM you have two paths:
I would try to get a B450 motherboard (you need to make sure the BIOS is up to date for Zen 2) and some of the following: Ryzen 5 3400G, Ryzen 3 3100 / 3300X (if you can find them), Ryzen 5 2600, or Ryzen 5 3600 (Ryzen 3 3100/3300X and 5 3600 are Zen 2).
If you wana go the intel way, then get at least an intel Core i3 10100, which is 4 cores / 8 threads, and you can put it in a newer H110, B460, Z490 motherboard and later on update higher tier chip or to the 11th gen intel chips when they launch. But yeah unless you spend more money on a Z490 mobo, you wont be able to run your memory at 3600MHz.