“plans.” The Hebrew word is machashabah (#04284 מַחֲשָׁבָה), and it can refer to a person’s thoughts, or what he thinks about, that is “plans.” In this context, it seems “plans” fits best, as also most modern versions say as well.
“will be established.” This is one of the “ideal” verses in the Bible that is often true but not always true. This promise would be fulfilled here on earth today if we lived in a godly world with godly people, but we do not. The Devil is the god of this age (2 Cor. 4:4; 1 John 5:19), and there are many evil people, so the plans of godly people are often foiled. This promise will only be fully fulfilled in the future.
[For more on promises like this, see commentary on Prov. 19:5.]