This is what I would expect to agree with an advanced player at the partnership desk given that we have only a few minutes to discuss all of our agreements and want to stick with what I would expect both of us to be familiar with.
If opponents bid 2C or a double, systems are on, double of 2C being Stayman. If 1N is naturally doubled, redouble is to run out to 2 of a minor; if 1N is artificially doubled, redouble suggests penalizing them.
Otherwise, 2N is the Lebensohl convention - it requires partner to bid 3C, after which I can show a weak (i.e. less than invitational) hand in a suit I could not have bid at the 2 level (other than the opponent's suit) or an invitational hand in a suit I could have bid at the 2 level. A bid of 3N is to play, but denying a stopper in their suit; 2N followed by 3N is to play, showing a stopper. Analogously, a bid of their suit is Stayman without a stopper; 2N followed by their suit is Stayman with a stopper.
(There are various alternatives to Lebensohl, some of which are genuine improvements, but none of them are even close to being known by all advanced players.)
Otherwise, 2-level bids are natural and intended to be passed, and 3-level bids are natural and game forcing.
Double is negative, showing a hand short in the opponent's suit, without an obvious suit of our own to compete in, and less than game forcing strength. (A substantial but shrinking minority still prefers double to be penalty.)