Few things to consider:
1) Faster shutter speeds help you overcome blurring in a photo and blur is something that cannot be corrected in editing* So when shooting a subject which will/is/might move a fast shutter speed is always a prime requirement.
2) If you use a high ISO you will get more noise in the photo. However if you underexpose a photo and then bump up the brightness in editing you will reveal far more noise from ISO than you would have got if you'd used a higher ISO and gotten a good exposure.
Note that you'll want to look up the theory "expose to the right". This relates to your histogram and presents an exposure theory to consider when shooting which suggests that you want to, whenever possible, overexpose your photos to thus capture the most light data for working on (since you lose nothing if you simply darken areas).
Note that this theory states overexposing, but with the limit that no point on the photo should be blown out (ie where the camera just records white data and no details).
3) Noise reduction software can help with a lot of situations in reducing the noise in a photo; also note that resizing for internet display and printing will often hide much of the noise as well; so sometimes it's not half as bad as you think it really is.
*in very minor cases you might be able to fix the problem; but it will require extensive use of the clone and heal tools. In addition whilst you can theoretically remove any blur it will typically result in having to rebuild large areas of a photo and thus be more digital art than photography (at the hours it will take you might as well just draw rather than take the photo)