You have got me some what confused because i only have a camera but no additional lenses and as far as i can tell i cant change my exposer on my camera. I have only just started to take pictures. I dont understand what you mean by Greater depth of field or by smaller aperture (larger f-stop). My camera is auto focus it self and i have no control over that unfortunally which means sometimes shoots are ruined by it not focusing properly.
Sorry to confuse you. According to online reviews, the S3500 does give you control over the exposure, but you may have to do some reading in the manual, or playing around with the camera, to find out exactly how.
Background: Cameras have two basic methods for controlling how much light reaches the sensor, and therefore how bright or dark the picture is. The camera can control how long the shutter is open for (shutter speed), and it can control how wide the opening in the lens is that light comes through (the aperture). A slow shutter speed (e.g. 1/60 second) means a lot of light and a bright picture, while a fast shutter speed (e.g. 1/500 second) means less light. Similarly a wide aperture means lots of light, and a small aperture little light. (Confusingly, aperture is measured by F-stop, with large F-stops meaning small aperture. On your camera, a wide-open aperture is F2.8 or F3.0, and the smallest aperture is around F8.)
When you press the shutter, the camera measures the amount of light and picks a combination of aperture and shutter speed to give what it thinks will be the right exposure. Sometimes it guesses wrong, however, and either underexposes or overexposes something in the scence. When that happens, you can use exposure compensation, which just means you tell the camera to expose more (+ compensation) or less (- compensation) than it thinks it should. Somewhere on your camera is (I gather) an exposure compensation button, which should let you adjust this. (Note: one full unit of compensation is equivalent to doubling or halving the shutter speed.) So that's a way of handling blown-out highlights, as you have on some of your white flowers: if you see that your picture looks overexposed in an important part of the picture, dial in some negative compensation and take the picture again. (Another note: the histogram, which I believe you can access by holding down the exposure compensation button, is a powerful tool for judging whether your picture is well-exposed -- but I don't have time to describe how to use it at the moment.)
So that's exposure . . . What about depth of field? There's more to the choice of F-stop and shutter speed than just getting the right amount of light. There are trade-offs. A slow shutter speed (with a narrow aperture) may give you a blurry photo, either because the subject moves while the shutter is open, or because the hands holding the camera shake. So a faster shutter speed is often good. For a faster shutter, however, you have to have a larger aperture, and a larger aperture means less depth of field. The depth of field is the range of distances over which subjects are still in focus. For example, if you focus on something ten feet away, objects 9 feet and 11 feet may still be in pretty good focus, but ones 7 and 13 feet may not be. The larger the range that's in good focus, the larger the depth of field. A big depth of field is often (but not always) desirable, since it makes it easier to keep your whole subject in focus.
So, as I said, it's a trade-off. Large aperture will give you big depth of field and good focus, but also a slow shutter speed and possible camera shake, while a fast shutter speed makes for crisp pictures with narrow depth of field. If you take control of the camera, you can at least choose which you would rather have, rather than letting the camera pick a combination. I believe your camera has an "aperture-priority" mode, which lets you choose the aperture (remember, large number = small aperture), and then lets the camera pick a matching shutter speed. Try experimenting with different apertures to see the effect on depth of field. (Your camera does not a have a great range of apertures, but you should be able to see the difference.)
Of course, if there isn't much light, you can easily find yourself in a situation where you can't get both the depth of field and the fast shutter speed you need to take the picture you want. Ideally, at that point you plop the camera on a tripod and use a slow shutter speed. If you don't happen to have a tripod along with you, you just do the best you can.