I agree with Adrian's definition of double standards. Joey wants to know, "Why is it okay for you, but it's not okay for me?" Phoebe has one standard for herself -- it's okay to worry about her appearance because she's a woman -- and a different, "double" standard for Joey, who is suddenly "high maintenance" (too much effort) when he starts to worry about his appearance. When Phoebe says "they have us picking out china patterns," she means "they're acting like we're getting married." Good china tableware is a traditional wedding gift in America, and it's fairly common for people to shop together when they get engaged to look for a pattern (or design) that they both like. I assume Mike gagged because he felt uncomfortable at the thought of getting married, but I don't remember that particular episode. I hope that's helpful. Good luck with your studies!

'Double standards' refers to a situation in which a person [or organisation] maintains that others should follow certain rules of behaviour, but the person [or organisation] itself does not follow them. From the short excerpt of the script that you quote, I would guess that "pick out china patterns" is referring to the girls' feeling that they are now considered by the boys to be part of the household, even though they "haven't even moved in yet" : they are suggesting that they are being asked to choose [pick out] styles [patterns] for possible domestic items to buy [china i.e. plates, cups and saucers, etc.]. [These items are referred to as 'china' because fine ceramics were imported from China at a period of history]

To pick out China patterns means “Planning a wedding”