YOU SAID:

lets go shopping then go home and get some grub

INTO JAPANESE

買い物に行って家に帰って食べ物を買いましょう

BACK INTO ENGLISH

Let's go shopping and go home to buy food

INTO JAPANESE

買い物に行って、食べ物を買いに家に帰りましょう

BACK INTO ENGLISH

Let's go shopping, let's go home to buy food

INTO JAPANESE

買い物に行きましょう、食べ物を買いに家に帰りましょう

BACK INTO ENGLISH

Let's go shopping, let's go home to buy food