So you've read The Art of Photography, you've discovered that it doesn't matter what camera you own, you've acquired a camera or two, you've downloaded some free photo editing software, now what?
The most common accessory you may want to consider are filters, which screw on the front of the lens. There are a bunch of different ones that do a bunch of different things. Some common types are UV, polarizing, warming or cooling, yellow, orange or red when shooting black-and-white, and neutral-density (including graduated neutral-density). There are many others, and different verieties of each.
Do you need filters? No. Is it a good idea to own some? Yes.
It's hard to say which ones you should get and which ones you should avoid, because they all do something. So it depends on if what you are photographing benefits from the use of a specific filter. It might also depend on if you can easily replicate the effect of the filter later in photo editing software (you may not want to spend the money on the filter if you don't have to).
Camera stores are quick to sell UV filters, but in reality they do very little. That is not to say you should not buy one, but be aware you are getting little more than a lens protector. Yes, UV filters remove small amounts of haze from an image, but it's not noticeable in most cases. It is best to spend your hard-earned money on something that actually visibly improves the photograph.
Polarizing filters darken blue sky, slightly increase saturation, and remove reflections. Warming filters are good to have if you are using color film. If you are using black-and-white film, you should have a yellow, orange or red filter (or, perhaps, all three). A neutral-density filter could come in handy when photographing moving water. Graduated neutral-density filters might help you when the dynamic range of what you are photographing exceeds the capability of the medium you are using to capture it.
Which should you own and how many are questions only you can answer. The answers will depend on what you are photographing, what you are using to photograph it, and what you want the image to look like.
Learn what each filter does and decide if you would commonly use it or not. You might decide you have no need for filters. You might decide you need a lot of different filters.
A basic kit might include a polarizing filter, warming filter and orange filter. If you just have a DSLR (and not a film camera), a polarizing filter and graduated neutral-density filter are good options.
The filter size will depend on the size of the lens. Look at the front of your lens and you'll see a number (52mm, for example), be sure the filter size matches. You'd hate to spend money on something that doesn't fit.
Some photographers use tripods most of the time, while others never use them. They certainly come in handy in low-light situations or when using a long telephoto lens. If you don't own a 300mm telephoto lens and don't plan to photograph in the dark, you probably don't need a tripod.
My suggestion for most photographers is to buy a cheap one because it will be light-weight, fold up small, and, if you find that you rarely use it, well, it didn't cost much. If you decide that the cheap one isn't good enough, you can always upgrade later.
Cheap tripods are not always as steady as you'd like them to be, so you need to move yourself away from the camera to prevent accidental movement. Yes, even pressing the shutter release button can cause some slight and unwanted movement on long exposures.
The simplest (and cheapest) fix is to use the camera's built-in self-timer. Some cameras allow you to adjust the length of the timer to as short as you want. Another option is a remote control. I'm quite happy with the remote I purchased for my DSLR from ebay for less than $10. You can even use your universal TV remote to operate your camera. Also, a cable release cord is an option for many older cameras (and some newer cameras, as well).
If you don't like lens flare, you probably want to purchase a lens hood. If it is not in your budget, you can always craft your own with construction paper and rubber bands--or a yogurt container.
Personally, I like lens flare and I think--if you can find ways to use it creatively--it can add interest to the composition. However, many photographers will go to great lengths to avoid lens flare at all costs.
Most cameras have a built-in flash, and most built-in flashes do a good job of fill-flash. Depending on what you are photographing, there is a pretty good chance that is all you need.
Should you need to purchase a flash, look on e-bay and you can find a decent one for under $25.00, including shipping. Should you need studio lighting, here are some good alternatives to spending large dollar bills on "professional" equipment: here, here, here, and here.
I have two: one that is a backpack and can hold several cameras, and a smaller one that can hold only one camera. I'm not overly happy with either, but they both get used and adequately perform the job of keeping my equipment organized and safe. Unless you find a camera bag that you know is the one you will love, I would not recommend paying full price or spending large sums of money on this. Shop around and find a good deal.
Now get out there with your camera in hand a photograph the world around you!