i got a 20g super basic super budget setup, ill attach a pic later for reference. What I learned is that HOB filters are super underrated. I was able to keep acros, LPS, nems, zoas, basically every kind of coral in my 20g by using a HOB filter, jebao pumps, and a SMATFARM light, which i got for 150 on amazon. I recently upgraded so I moved most stony corals to my larger tank, and left the nems and such in my 20g. when I did have a larger coral load in the 20g, I would just do larger waterchanges and not dose anything until it got to the point were I was losing 1 DKH every couple days, in which i just dosed baking soda. your pretty limited with fish options, so I stuck with clownfish, lawnmower blennies, firefish, dragonets, chromies, and inverts.
As for cycling and such, you only need a small piece of liverock from someone elses tank to seed your tank with bacteria, the cycle would take a week or so if you were to add in a fist sized chunk of aged liverock from someone elses tank.
dont just throw rocks in there, you wanna actually enjoy your rockscape and consider the coral growth and leave space for the glass to be cleaned.
ATO is extremely important in such a small tank, dont skip waterchanges down the line or water testing, because you got such a small volume of water its easier for things to go bad.
In short for coral you can basically get anything as long as you go with the natural progression of your tank,
as for fish:
your super limited but you can get
PJ or banggai cardinals
clowns
baby fish such as engineering gobies, some types of angels, some super small baby tangs like tomini or mimic while they are young but eventually you need to sell/trade/upgrade
lawnmower blennies
small blennies and gobies
dragonets