I typically do 3-gallon AG. My equipment purchases were driven by upgrading from my starting point which was 5-gallon extract batches, so I’m not sure if my set up would what I’d use if we’re making a “right sized” 3-gallon system from the start.
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Brew pot. I have a 20-quart pot; a Hamilton Beach stock pot, IIRC. This can be a bit scary at the start of a boil; I’d go jut a little bigger if I could, but I have a microwave oven mounted over my stove so clearance is an issue. As it is, I spend a LOT of the brew wiping condensation off the bottom of the microwave. Still it’s better than freezing my @$$ off in the winter, or sweating like a pig in summer.
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Mash tun. I use a round 7 gallon cooler. The wife and I go for an exercise walk during the mash, and it holds mash temps within a degree for the 80-90 minutes we typically leaving it. I use a BIAB bag in the cooler versus a false bottom, but I did invest in a ball valve because that thumb squeeze thingy was just terrible. False bottoms are available for the round coolers, and bazookas can be fabricated. My opinion, is that the BIAB makes for easier cleanup. A larger pot would be a substitute, but I think the cooler wins on price and convenience for me.
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Fermenters. I have a couple 5-gallon BMBs that were purchased as secondaries for 5-gallon batches. A bit smaller would be fine, but I have zero blow-off concern. I added a couple 3-gallon better bottles for those times I still want to have a secondary. I would not recommend using anything less than 4-gallons as a primary for a 3-gallon batch.
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Wort chilling. I use an immersion chiller. I don’t think there’s much difference between 3- and 5-gallon batches in terms of chilling equipment, but 3-gallons can be chilled easier than 5. I suppose an ice bath in the sink is still practical for 3-gallons, but I don’t do that.
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Fermentation temp control. I have 7.1 cu ft freezer, that can hold 2 buckets, it still only holds 2 of my 5-gallon bottles, I’m not sure if a smaller size freezer would do for smaller batches, but the price jump between the 5 and 7 cu ft freezers is minimal. The square 3-gallon better bottles, fit side-by-side, so I could have at least 4 in there, maybe 6. To control the freezer, I went super nerdy and built my own controller from scratch, using a Raspberry Pi. I wouldn’t recommend the PI as a controller platform, as it dies every time the SD card wears out. 2-stage controllers can be purchased with much less aggravation.
