You might be tempted to go buy a bunch of equipment but you can get really far with the basics once you've learned good technique:

• a decent paring knife and 10" chef's knife (Victorinox fibrox are decent quality and not too expensive as knives go)
• an end grain wood cutting board
• a medium sauce pan
• one or two sheet pans
• one 8" or 10" stainless steel skillet
• a spatula and some wooden spoons
• a pair of tongs
• stackable measuring cups and spoons

That will get you very far. If you find you're enjoying cooking and want to improve your kit, you can add things as you need them (whisk, masher, boning knife, stock pot, etc.). Try to avoid buying unitaskers. You can mince garlic with a knife, so unless you're mincing a ton of garlic, a garlic press is probably not a good investment because it only does one thing.

There are a ton of video tutorials for learning knife skills online but if you want something printed, Henkels has a Complete Book of Knife Skills that I've found very useful.

You'll want to keep your knives sharp. You can learn to do it yourself with a double sided 400/1000 water stone and a video tutorial. A ceramic pull through sharpener will do in a pinch but they're pretty hard on the knives. Metal pull through sharpeners will destroy the edges of your knives, so don't buy one of those. Also don't use anything motorized because the heat can damage the heat treat and wreck your knife.

You will read on the Internet that cast iron is the One True Material for skillets and frying pans. People who say this are in a cult. Cast iron pans are great for searing because they retain a lot of heat but stainless clad aluminum will give you better control and more even heating, Teflon will give you better non-stick performance, etc. Personally, I reach for my stainless steel skillet most often, which is why I recommended it above. You may also read that you should never wash cast iron with soap because it will ruin the seasoning. This is bunk. The seasoning is chemically bonded to the surface and you can't scrub it away unless you're physically removing material with hard abrasives or caustic chemicals. Soap and a scrubby will not hurt your pan. Do thoroughly dry anything cast iron after you wash it, as it will rust if you don't.

There is probably a restaurant supply in your area and they are probably open to the public. That's a great place to get things like skillets, sheet pans, racks, ramekins, tongs, etc.

Pick up (or borrow from the library) a cookbook that teaches cooking technique through recipes. These are some of my favourites:

• Ruhlmann's Twenty - Michael Ruhlmann
• The Food Lab - J. Kenji Lopez-Alt
• Salt Fat Acid Heat - Samin Nosrat