For testing, I'm using the Zotac GTX 1060 3GB Mini -- and yes, after fiddling withe some of the bigger cards, it's positively tiny! If you're thinking of building a someone more compact miner, maybe this is a good choice. But with a single fan, cooling isn't as good, and mining performance is decidedly mediocre.
As noted before, you could safely run the 1060 cards with a 1000W PSU, which is a bit easier to find than the 1200W and higher models I recommend from some of the other builds. EVGA's 1000W T2 is a great Titanium rated power supply with a 10-year warranty -- sure to outlast your GPUs for mining purposes! -- but it's also more expensive than my standard 1350W Platimax recommendation.
I like math!
Basic PC setup: $870 (no case -- use a wire shelf)
Ryzen 5 1600: $230
Asus Prime-X370 Pro motherboard: $150
16GB DDR4-2667: $97
240GB SSD: $63
1350W PSU: $240
PCIe riser adapters: $50
Six GTX 1060 3GB cards: $184 each = $1,104
Total = $1,974, income of $10 per day ~= 197 days to ROI
Obviously, this isn't quite as much of a budget build as I could do with the 1060 3GB. If you go with a Pentium G4560 CPU, 8GB RAM, and a Z270 motherboard, you could shave off about $200 from the total. But even then, you're still looking at 177 days to ROI for the system. Buying RX 570 4GB cards is clearly a better way to go right now.