For dried, I like thyme, rosemary, bay leaves, oregano (I have both Mexican and Greek), mint, sage, lavender (make sure it's culinary lavender) and even basil I find acceptable for certain things.
Herbs like marjoram, tarragon, chives, parsley, chervil, cilantro, I don't think do well dried. They just don't taste the same. Marjoram for one gets a nasty soapy, almost fishy taste to it when it's such a lovely fresh herb. Parsley is all about its vibrancy, which is lost when dried.
Fresh basil is what you want 99% of the time. Dried mint is great, but at times only fresh will do.
So, I buy herbs when I need them for the most part.
Whole black peppercorns, whole coriander (the seeds, not what you call cilantro), bay leaves, smoked paprika, plain paprika, chili flakes (I suggest Aleppo if you can get them), cinnamon (whole and ground), nutmeg (whole only), star anise, ground ginger.
It also depends on what you cook. If you like Indian, then I suggest you also have cardamom, turmeric, mustard seeds, black cardamom, Garam masala.
ETA: Duh, forgot cumin seeds!
In general you want to stick to whole spices since they last longer and are more versatile. Much better to have whole cumin seeds that you can use whole or toast up and grind for whatever you need. Even garam masala you can mix your own, or buy a mix of whole spices.
If your ground spices have been around for a while (a year) consider re-purchasing. Five spice is a good one to refresh.