Gotcha. Low light isn't going to be a strong suit for sure...for high ISO work like shooting moving subjects - but as you said, you might be able to work around it.
The depth of field option is definitely one of the limitations of small sensors - or one of the benefits, depending on how you look at it. Small sensors = big depth of field...so it is hard to get a shallow depth of field look on a typical small-sensor P&S. However, you do have a big optical zoom on yours, so there are ways to get the blurred background...it just takes some technique. There are a few ways to do it - first off, the bigger the aperture the better - so if you use your camera's Aperture Priority mode, and make the aperture the smallest F number available, you will get the best chance to reduce the depth of field. Second, try getting as much distance between you and your subject, and as much distance between the subject and the background, as possible. By increasing these distances, you increase the chance of the background being out of focus. Third, use the zoom to get closer to the subject - with big telephoto lenses, the more you zoom, the shallower the depth of field will get. So by standing farther away and using the zoom to get closer, you can increase those distances and shallow the depth of field.
A quickie example I shot years ago with a camera similar to yours - a Sony H5 with a 12x zoom - I used maximum telephoto, wide open aperture, and shot a subject that was a good 10 feet from the background, which was enough to get that soft out-of-focus area:
Another way to get that shallow depth of field and subject isolation is to use the macro mode, get really close to the subject, use any zoom you can...macro modes are designed for very close focus and the depth of field will often narrow considerably even with a P&S camera.
Same idea used here with the old H5 ultrazoom - macro mode, got up close to the subject, didn't need to zoom very much, kept the aperture as open as it would go, and even with only a few feet to the background, the close-focus of the macro mode gave the softer background blur:
It's all possible with a P&S camera like yours...it just takes some learning, honing your technique, and a little bit of a work-around. DSLRs will make it easier to get such shots, or to do so without as much distance or planning...but it will still require the same basic knowledge and technique...so better to learn that first!
Sony DSLR-A580 / Sony 18-250mm / Minolta 50mm F1.7 / Sigma 30mm F1.4 / Tamron 10-24mm / Tamron 150-600mm / Tamron 90mm F2.8 macro / Minolta 300mm F4 APO
Sony A6000 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses