Peri is one of my favourite companions of all time.
I don't know why I like her so much. She's hot (even the present older version of Nicola Bryant is sexy), a bit funny, she's just a default companion to me with that nice little spark. Plus I like her chemistry with Colin Baker.
Plus I've never seen the Caves of Androzani, so I can't say anything about her in that.
The companion I don't really like for some reason (oh man I know I'm going to get trolled for saying this) is Sarah Jane. She just bores the death out of me, I find her annoying. The only thing I haven't minded her in is Planet of the Spiders, although she's been okay in the revived series.
I'd say my favourite companions are Ace, Rose, and Peri. Also a big Jack fan, but I don't quite count him as a companion.