There's a fair bit of context, off the top of my head -
Dramatic context (e.g. role of character in play), Authorial (Goldsmith), reader (audience), historical - role of women in society, marital views. Litarary context - SSTC as a comedy, a farce, well-made play structure.
Just a quick note mate - don't entirely focus on Kate, it'll be a real waste if a question on her doesn't come up, but by all means prepare what COULD be said.
For Kate, I would say - dramatic context, role of her in play, relationship with Mr. Hardcastle maybe, role of women in society, views on marriage.