You cannot use a B16A or B16B crank to achieve 1.9-2.0L. Even if you bore out to 87 mm, the displacement is only 1840 cc.
This leaves us with the remaining cranks:
I. B17A Crank (IF you can find one)
You will need to bore out to at least 86 mm to get close to 1.9L (1891 cc). Boring to 87 mm (max.) will get you 1936 cc but reduces your reliability. Using a compatible, direct-fit LS B18A/B rod onto the B17A crank, the rod ratio will be a very good 1.68.
II. B18A/B or B20B/Z Crank
For the B18A/B block, you will need to bore out to at least 84 mm to get close to 2.0L. If you do not want to re-sleeve, then a bore of 82 mm will give you close to 1.9 L (1880 cc). Most people opt for 84.5-85 mm bore to get 2.0L (1996-2020 cc) . You can do this by boring and sleeving a stock LS block or honing a stock B20 block (stock bore is already 84 mm!!!) to 84.5 mm (cheapest way to go).The rod ratio remains stock with 137 mm long stock rods at 1.54. There is no advantage to using a B18C rod, since this only increases the rod ratio to 1.55 and you'd need to add 0.9 mm deck height.
III. B18C Crank
You will need to bore out to at least 85mm to get close to 2.0L (1979 cc) and 83-83.5 mm to get close to 1.9L (1887-1910 cc). You'll have to re-sleeve anyway, so you might as well go whole hog with 85 mm. The rod ratio remains at 1.58.