Bacteria mainly produce lactic acid. Saccharomyces produces some succinic acid as a fermentation byproduct; this is how it adjusts pH, it's not enough acid to taste sour. Some yeast/bacteria can produce acetic acid if there is enough oxygen present and alcohol. Other organic acids come from plants.
Lactobacillus plantarum produces a clean and smooth lactic sourness. It's extremely easy to make delicious sour beer.
The kettle souring technique is a relic from when brewers were using wild bacteria to sour.
L. plantarum is extremely hop-sensitive and doesn't form a biofilm, therefore it doesn't need to be killed because there's essentially no risk of contaminating future batches. It works quickly even at lower temperature (anywhere between 65°F to 100°F), so it's great for co-souring and post-souring, and it produces a nice sourness down to around 3.1 to 3.3 pH, which is plenty sour.
It's very easy to add other acids if you feel the need to supplement the acid profile. You can buy individual acids, lots of them are used in brewing and wine making -- citric, tartaric, malic, ascorbic, acetic, lactic, and phosphoric.
You also have other "natural" options to add acid, like lemon juice or Granny Smith apple peels.
In my opinion adding extra types of acids is generally unnecessary. You can add complexity from the yeast, malt, water, and/or hops (I'm a traditionalist in that regard). The Lacto blend I use also contributes a good flavor.
I haven't fermented rice, so I defer to the others about how much acid the white Koji rice actually contributes. I do find it hard to believe you could make a sour beer just with a rice addition.
I live and breathe sour beer; happy to answer any questions