You could say 'I'm going to buy some food'. That would cover both the vegetables and the meat.
In British English at least, 'shopping' can mean food. When I go to the supermarket to buy food and household products, I say 'I'm going shopping'. I'd also refer to the purchases themselves as my 'shopping'.
This may not be universal, though. This reminds me of a time when I had a genuine misunderstanding with a fellow native English speaker. My family and I were on holiday, and were being shown around an apartment we were renting. The American lady who was showing us round asked if I had any questions, and I told her that I needed to 'get some shopping'. She proceeded to get out a map of the city, and she showed me a shopping mall that was several miles and a subway journey away. Suddenly I realised that she had misunderstood my meaning. She thought that I wanted to leave my suitcases and my family and go rushing off to the other side of the city, desperate to buy some designer fashions. She must have thought that I was mad! In fact, my needs were much more modest - I just wanted to pick up a loaf of bread, and maybe some milk and tea. I then had a quick think, and adjusted my vocabulary according to what I'd heard on American TV and movies. 'Umm....groceries?' I ventured tentatively. That did the trick! She immediately knew what I meant and directed me to a supermarket at the end of the road. Just wondering...does anyone else have any genuine examples of misunderstandings with native speakers within their own language?