Would like to know what are the best buys that we can bring back home in Beijing this June?

There are so many goods you could purchase in Beijing, such as the nice silk, handicrafts, pearls and jade. See this page to find a full list: https://www.travelchinaguide.com/cityguides/beijing/shopping.htm

As for food, of course the Beijing Roast Duck which enjoys high fame for a long time. Find more: https://www.travelchinaguide.com/cityguides/beijing/dining.htm