If you want to fly from Newcastle, look at jet2holidays they have free child places and good prices. Even though you are looking for next October, search the late deals section by entering your dates, departure airport and party size and see what comes up, hopefully within budget.
Not sure if you'll get AI in the school holidays for that price, and if you do, the quality might not be great, but its still a sunny holiday or I would look at hotel B&B or half board (we once got HB for £20 pp more than B&B).
I don't like a buffet for dinner so my interpretation of the best value/lowest effort/nicest experience is to do the following:
Stay in a hotel on a B&B basis and have a big breakfast as late as possible, eg 9.30 am. Pick a hotel that has a kitchenette, or a fridge at the very least.
Eat out once each day, in Spain lunchtime is good as you can get Menu del dia for less than evening meals and this is often served all day, or at least until 3/4 pm
For the other meal, have a snack such as an ice cream, chips, pizza slice or tapas. After a big breakfast and a big lunch, I'm happy with a small dinner.
Alternatively, have the small lunch and evening meal out, which ever works best for you. Go to the supermarket once or twice during the holiday to stock up on drinks, snacks, bread, ham, cheese etc, ice creams etc. Minimal effort - just make sure your DH also pulls his weight with food prep, it's not all down to you. And in a hotel there's no cleaning necessary, just a small amount of washing up.
In my experience doing it this way is cheaper than good quality AI and a nicer experience than mid range AI for about the same price.