Best "plug-ins" for inequality questions?

It really depends on the type of question you're looking at. A lot of different situations can crop up in GMAT inequality questions, so it's impossible to list any number-picking rules that will be applicable to every question. In general, most inequality questions hinge on negatives and positives. So when plugging in numbers, you normally want to pick numbers that will make any terms in a product or fraction positive and negative. For example, if you see this inequality:

(x-11) / (x-12) < 0

plugging in one positive value and one negative value for x is not going to tell you anything useful. Instead you want to plug in values that might make the numerator positive or negative, and the denominator positive or negative. Here the relevant numbers are 11 and 12, so you should plug in one number less than 11, one number between 11 and 12, and one number greater than 12. Then you'll see that the inequality above can only be true when 11 < x < 12.

Further, when you have inequalities with simple powers of x on both sides, we normally need to consider not only positives and negatives, but also fractions near zero (both positive and negative). That is because values near zero behave differently from whole numbers when we raise them to exponents. For example, if x = 2, and we then cube x (that is, find x^3), we get a larger value. But if x = 1/2 and we cube x, we get a smaller value. The same occurs with negatives; if x = -2, and we cube x, then we get a smaller value, but if x = -1/2 and we cube x, we get a larger value, since -1/8 is larger than -1/2. So if you see an inequality with simple powers of x on both sides, like the following:

x^3 > x

then you'd normally want to test four values: one value less than -1, one value between -1 and 0, one value between 0 and 1, and one value greater than 1. You then find that the above inequality is true when -1 < x < 0, and when x > 1.

I think a lot of test takers end up in 'traps' when they use number-picking for inequality questions. It can be a reliable strategy provided you know exactly which numbers to test. But if you miss one exceptional case, you can often get the wrong answer by number-picking. If you understand the algebraic rules for manipulating inequalities, those can often more reliably (and more quickly) get you to the right answer.