There really isn't any need for fancy gizmos and gadgets; just a few well made simple tools and the knowledge of how to use and care for them will take you far.
A skillet: Others may view this differently, but skillets fall into 3 groups. Lightweight, medium weight, and cast iron. In the lightweight category, you have your anodized, non-stick aluminum. Aluminum, with its high thermal conductivity but low thermal capacity, is perfect for delicate cooking (eggs, fish, shrimp), but can certainly take on some heavier tasks like sautéing veggies and cooking chicken & steak. The thing to note about the latter is that is can be hard to get a nice brown crust on your food. These types of skillets are often pretty affordable.
In the medium weight category, you have solid steel or aluminum clad skillets. Steel has poor thermal conductivity, but pretty good thermal capacity. The main difference between full steel and aluminum clad skillets is heat distribution/hot-spotting. Aluminum clad skillets provide more even heating, but they come with a higher price tag. Medium weight skillets are the jack-of-all-trades; you can pretty much cook whatever in them. One thing to note however is that they often are not non-stick, which means cooking things like eggs will leave you scrubbing in the sink.
Cast iron. If cast iron were human, it'd be a powerful cult leader. While my cast iron pan is one of my favorite things to cook with, it does require a certain level of devotion. The internet has enough people extolling cast iron, so I'm going to leave it at this: I do not recommend it as a starter skillet.
Final thoughts on skillets: Regardless of what you choose, proper care will always extend the life of your cookware. Most metal skillets can't handle metal utensils. Metal will scratch the surface, causing food to stick more easily, and over time will significant diminishes the quality of your cookware. Opt for wood/bamboo or plastic/silicone. Never use steel wool or a scour pad on your cookware, and only use non-abrasive sponges. Similar to metal utensils, this will scratch your skillet. Never let a dirty pan sit out, or be submerged in water for too long (especially cast iron); over time it will degrade your skillet and make it harder to clean, which will make you want to use those metal scour pads.
Utensils: For all your stirring, flipping, and scraping needs. Opt for wood/bamboo or plastic/silicone, avoid metal (unless it's covered by silicone).
Knowledge: I'm not trying to be a motivational speaker; an understanding of why those steps in your recipe matter will help you eschew recipes all together. Learning about your tools will give you greater control over them.
Curiosity: Baking is a science, cooking is an art. Get creative, experiment, and enjoy yourself!
Final thoughts overall: "You get what you pay for" definitely holds true for cookware; but paying more doesn't mean you're paying for an appreciable increase in quality. You don't need a name brand, but consider spending a little more for something that'll serve you better and last you longer. I'd like to stress one final time that cooking is less about what you have, and more about what you know; The greatest way to learn? Practice & experiment!