I would definitely buy at least one type of vinegar as that's helpful for salads, marinades etc. Also, depending on where you are, it might be nice to pick up something local, including fresh herbs, chilli, garlic, ginger etc. My mum always used to pack a couple of her favourite jars of herbs/spices that she used all the time. If it was me, I'd probably rely on fresh herbs so would just take fennel seeds, paprika, cumin and cinnamon and oregano but that's me.
Assuming good weather and BBQs a lot, I think you can do a lot with salads and a few basic flavourings .eg we did griddled aubergines on the BBQ this weekend and then I made a little dressing of just some olive oil, garlic, red wine vinegar and fresh chopped chilli and mint and I topped the whole lot with some rocket and mozzarella. Was delicious and those are all ingredients you could buy easily.
An easy marinade for chicken without lots of extra ingredients:
Olive oil
Lemon
Ketchup
Garlic
Paprika
Fennel seeds but skip this if you can't be assed to buy some.
Stir fries are easy and don't need a lot of spices outside of fresh garlic, ginger and mint. Buy a stir fry sauce of create your own flavouring with lime juice and soy sauce.
When we are self catering, we almost always do at least one night of spaghetti bolognaise as it's an easy one to make and doesnt have to have a lot of additional flavourings. I usually add dried oregano and basil, but could swap that out for fresh or just basil.
Chicken tray bakes can be done with very limited additional flavourings. Lemon goes a long way in these situations. Some chorizo or parma ham can add a lot of flavour without the need to add herbs/spices and some fresh garlic goes a long way too.