Some very basic things: grill a burger, roast chicken parts, grill a flank steak, bake a potato, cook rice and make scrambled eggs. Try one of these every week and start when you're rested, attentive and not in a rush. If something goes wrong, it's only food and you can try again next week. Everyone screws up in the beginning.
Kitchen essentials; a nonstick omelet pan, a sauce pan, a grill pan, measuring cups, measuring spoons, a silicone spatula, metal tongs, a slotted spoon, a cookie sheet, some mixing bowls, a whisk, a peeler, a colander, a strainer, a can opener, a silicone brush for basting, If you want to get fancy, get a dutch oven, too. This sounds like a huge investment but you can get everything except the cookie sheet, pot and pan at the Dollar Tree for $1 each.
When you decide to upgrade your collection, go to Oxo for small utensils. I think cheap can openers and parers are really annoying. Oxo and Mueller have vegetable choppers that will change your life. It's like a little veggie guillotine that yields perfect cubes of celery and onions.
I haven't specified a cookware brand but I don't think you have to start with the top of the line. Go to Target or Costco and lift the pans and see how comfortable you are with the weight and handles.
The secret of the chicken is the right rub. The flank steak is about marinating and cooking to the right temperature. The rice has to be rinsed first so the starch won't make it glop together. Very hard to mess up a baked potato. An omelet takes time but scrambled eggs are easy peasy; The burger is about the right percentage of fat in the meat and not squashing it so the juices run out. Read about five recipes or look at videos before you attempt each of these. The best will explain the processes--how much heat and for long will it take to get a nice char on your steak or burger without turning the proteins to ash.
Your next thread should be what to stock your pantry with--oils, canned goods, bread crumbs, stock, spices, etc. Maybe you can split quantities with a friend. Martha Stewart has lots of pantry lists.
For knives, go to Amazon and look at their budget recommendations. You can trade up later. Amazon also has a great little thermometer that folds like a switchblade. It's only about 15, You really need it for meat.
Take it slow. Have fun. Forget about your mother's lousy cooking. It has nothing to do with you.