It's "china patterns." Traditionally in the US, when couples got married, people wouldn't give them money (in fact, giving money was considered very rude). People would give them household items, things like pots & pans, forks, plates, towels, bedding, etc. All of the things that the newly married couple would need in their new home. One thing they would need is plates and cups. Very fancy plates and cups are called "china" (or "fine china") and they're very expensive - so expensive that most people might buy a plate or two as a gift, but not all of the plates needed to serve a meal. So, before the wedding, the couple would go and look at all of the different designs that were available and decide which ones they wanted (picking out china patterns) - people could then go and buy the dishes for a wedding gift. It's not something that you do when you are in a casual relationship - it is something that people only do after they are engaged and going to have a wedding very soon. "have us picking out china patterns" means "think of us as almost married."

There was a question about it on here: https://www.italki.com/question/304439