Your (minor) ‘set’ is the particular sub-group of people with whom you’re dancing – often multiples of two couples. Formations can be: longways (‘proper’, ‘improper’ or ‘Becket’), crossways, circular or square. Square dance sets comprise four couples.
For ease of interpretation, terminology used on this site is consistent with heteronormative convention.
One’s ‘partner’ is the person - usually of the opposite gender - with whom the dance was commenced. When a couple are side-by-side, the lady is on the right. Also explain: ‘corner’, ‘neighbour’ and ‘opposite’… and ‘galop’ (a two-step chassé) 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 equalled.