Go to your local fishing shop. They usually can give you some solid advice. Good fishing gear does not have to be expensive, even for larger fish. Once you get really specialized, you might need an edge. Until then it is smooth sailing.
If you really just want to go fishing about four times a year, grab a light to medium spinning rod, a light to medium spinning reel, some 15lbs braid. Get some of the mentioned lures below, floats and sinkers, a fine selection of hooks, some split shot, and you are set for everything. Once you get hooked (hehe) and look further into fishing, you will see what you should focus on. With your allround gear, you will have a nice foundation to start with.
Coming from Europe, I know that bass fishing is a big thing over in the US. Fun fish that basically bite everything that moves through the water. Depending on your local bodies of water, you could start with this target fish, and somewhat specialize. But you did not specify what kind of fishing you would like when "regular" fishing. Thus I will try to cover some of your options.
There is what some call "active fishing" and non-active fishing, for which I have never used or heard a term.
Active fishing is everything where you actively guide your bait, like artificial lures, spinners, wobblers, and what-not (the list of these kind of lures becomes very long!). Fly fishing falls under this category as well.
Advantages of active fishing is that you can be very spontaneous and have only little requirements of your fishing spot. You don't need space to sit and stash your equipment, you can fish almost any depth and water vegetation, and since you always have your lures in your tackle box, you can go fishing anytime.
You are mobile and can move a lot, and you might feel exhausted after a long day of fishing.
The "non-active" style of fishing, for which I don't know a term, revolves around presenting a bait to the fish, and waiting for them to bite. You can use floats, special rods with soft tips, or electronic tools to notify you of fish biting. Personally, I love fishing with floats. This kind of fishing can be very relaxing, you enjoy nature, the silence, but are always somewhat focused of your float. This is pure meditation.
Now, these two kinds of fishing have different requirements on your gear. For active fishing, you need a rod that fits the weight of your lure, allows you to feel your lure working in the water, allows you to feel fish interacting with your lure, allows you to guide the lure and reel in the fish properly. While you certainly do not need expensive gear, your gear must fit your lure, target fish, and style of fishing.
For the non-active style of fishing, your rig does most of the work. Your gear must be able to handle the fish, but apart of that, you could use a stick as a rod.
Alright, lets get you equipped. I will not go into all aspects of fishing rods - it's just too much. I will just tell you what you need, but you might want to get some consulting in your local shop.
For active fishing, you must think about your target fish and the baits you will use. For smaller fish, you will use fine gear. For bigger fish, you will use heavy gear. Active fishing usually is on the fine side. These rods are light and thin, but often relatively stiff. This way you can guide and feel your lure. Keep an eye on its lure weight (if that is the correct term in english. The ideal weight range to use the rod.). It should somewhat match your lures. Slap a reel on your rod that somewhat fits in size. I could go into many details, but after all the reel will not really make or break your fishing experience. Go with a stationary reel. For your fishing line, you can go with mono or braid. I would use braid, but you can use mono as well. Again, this choice depende on your target fish, get some information in your local shop. They will also be able to tell you the appropriate strength. You could just go with some 15 lbs braid. This is overpowered for most target fish, but braid line is fairly thin, so it won't make much of a difference.
Finally, you would need some lures. Get some spinbaits your some easy throw-and-reel-in fishing. Get some soft bait and sinkers for some slower fishing (you throw and then reel slowly, or just pull with your rod, work the bait). Get some hard bait for more advanced fishing. I can not go into more detail without going too off-topic. There are too much poosibilities
Now to non-active fishing. Unless you use the tip of your rod as bite-indicator, you can use any rod. It should match your target fish (too light, and big fish might break your gear. Too heavy, and you won't feel anything. "Feeling" the fish can make the difference between losing or not losing a fish.) Pick an appropriate reel and line, you could get some fluorocarbon (supposedly "invisible" leader once submerged in water) to get an edge, or just leave it.
Depending or your style of fishing, get some floats, split shot, sinkers, hooks. Your hooks should match your bait in style (for example worm hooks for worms), and you target fish in size. Your sinkers (for some ground fishing for example) should match your rod and waters in weight. Moving waters require larger weight to stay stationary (there is much more on this topic, but i'll leave it at that). Your floats should match your target fish, fishing distance, and bait. If you fish fairly close to you, you can use smaller floats. Bigger baits and larger casting distances require bigger floats. Again, get some information from your local shop.