For ease of interpretation, terminology used on this site is consistent with heteronormative convention. Boundless confusion and disruption to a dance event can be caused by a caller’s use of unfamiliar, gender-neutral terminology in an attempt to satisfy the ‘woke’ community.
Your (minor) ‘set’ refers to the particular group of people with whom you’re dancing. Formations can be: longways (either ‘proper’, ‘improper’ or ‘Becket’), crossways, circular or square. Square dance sets comprise four couples. In Contra, a minor ‘set’ normally has two couples.
One’s ‘partner’ is the person - usually of the opposite gender - with whom a figure was commenced. When a couple are side-by-side, the lady is on the right. Also explain: ‘corner’, ‘opposite’ and ‘neighbour’… and ‘galop’ (a lively ‘side-close') v. ‘gallop’.
This handy,
document (courtesy of Martin Sutton, Stokesley

) and these
videos are valuable terminology references.
Country dance accompaniment can be: reel (say "double-decker" - supports a smooth walk), jig (‘bumpier’ than a reel - say “didily-dee” - encourages a bouncy, skipping step… or, for a double jig, say "didily-didily"), hornpipe (step-hop)… occasionally polka (step-close-step-hop/pause), or double-reel (rant step).
Normally, dances are structured to have a ‘revolution’ (repeat period) of 32 bars (usually equating to 64 beats - or steps) - comprising four, 8-bar figures (aligning with four, 8-bar musical phrases), designated A1, A2, B1 and B2, i.e. four phrases (usually) of 16 beats. Slip jigs are unusual, their bars comprise three beats ("didily-didily-didily" - 9/8 metre) and encourage three running steps to the bar. A few dances have revolutions that are other multiples of 8 bars long - say, 16 or 48 bars.
Dance tempos are roughly 120 beats per minute (bpm) (except for ‘step-hop’ hornpipes), so a single revolution of a 32-bar dance could last about 32 seconds (except for hornpipes and slip-jigs).
Suitable, recorded tunes for each category of accompaniment are suggested, but for an event, the flexibility and atmosphere afforded by live music can't be matched.