If it is a helpful frame of reference, Amanda and I used to spend about $50 a week on food (we actually budgeted $240 for the month), under a similar plan to yours: plan out your meals, at least dinners, slow cooker once or twice a week, vegetarian once or twice a week (meat is expensive!), grocery shopping once a week (which requires keeping a shopping list of the things you run out of or need in advance).

Now that we have another mouth to feed, we're a little higher at $300/month.

That didn't include any eating out we did for lunch or dinner though (which isn't often), so if you are looking for a total budget with no eating out, it will be marginally higher.