A good chef’s knife, paring knife and a serrated knife. 

A couple of different sized sauce pans, skillets (8”, 10” fry pans), high temp oven-safe Dutch oven (I have Calphlon one— Le Cruset is not in my budget), a grill of some sort (we have Weber gas started charcoal grill), iron skillet is great but not necessary.  Cookie sheet and cooling rack.

Mixing bowls— glass, stainless or bamboo composite.

Measuring cups and spoons.

Colander/Strainers.

Silicone spatulas— one hard for flipping, one softer for scraping. Wooden spoons (one that’s got a straight edge is good for stir-frying); slotted spoon; tongs; peeler; masher (with small holes works best); ladle; microplane grater (zester), larger grater; pastry brush (good real bristle paintbrush).

Food processor, blender, mixer.  Don’t need most expensive ones.  Some hand-held mixers have stands and different attachments.  I love my hand-held 3-in-1 tool. Has immersion blender, mini chopper and whisk.  Great for making soups/sauces, chopping onions, whipping cream.

Salt and pepper mills. Mortar and pestle.

Check out tag sales, ebay, Target, Amazon etc.  I got my KitchenAid Standing Mixer at a tag sale for $65!

Of course, there are more gadgets and appliances out there, but I think this is the core you’ll really need.

Good luck!!