In general, a point of sale system used to check your ID when you buy some soykaf and a cheap pair of sunglasses could be considered a public terminal. (Roll 2 dice vs your fake ID's rating). I like this option because otherwise your fake ID are only going to be good for a few dozen purchases before they get burned.
The best you can start with is 4. You need to run your SIN every time you buy something, pay rent or do a million other little things. Treat all ID scanners as security devices and the first time you use your fake SIN it's a 50/50 chance that you've just thrown away 4000 nyuan. If you instead treat them as business terminals, it's still only a matter of time.
Or you could, as a house rule, have the fake ID's rating be the threshold for the ID scanner's check, rather then an opposed roll. So your high end fake SIN could be reasonably expected to work for every day life, and only get burned if you use it to travel or draw enough attention for a serious inquiry to be made. (IE: You walk into a stuffer shack to buy soykaf and they run your ID on their business terminal to check it and authorize payment. Roll 3 dice to get a number of hits equal to your SIN's rating.. so if you spring for a rating 4 fake SIN, you could do this every day without worrying too much.)