Kiffer is a slang word for aimer (to like). Apparently it comes from the Moroccan Arabic word kif (كيف), meaning hashish (another Arabic word, meaning “grass” or “hay”). The semantic link between the Arabic word and the French slang term is that hashish provides pleasant feelings. Therefore a kif (used as a noun) is a pleasant experience, and kiffer means to like something or find it pleasant.

Regarding “choupé”, I’ve never heard of it but you might have actually heard the verb choper. It is a familiar word meaning “to catch”, and in the same context and slang language level as kiffer, it might mean “managing to get in a relationship with someone”. An English word with a somwhat similar meaning and usage is score, though choper is less strong, it does not imply any specific act, it can be as short as a single kiss.

Both words are slang words, mainly used by teenagers and young adults.

“Choper” is usually a synonym of “prendre“.

The context was somewhat weird — we were talking about girls, discos and all those manly stuffs that guys talk about

In this context, it likely means “have a sexual relationship with [the girl]”.