I always use the "Save As" Dialogue (Control+Shift+S) for exporting in the JPEG format. The resolution of the resulting JPEG will be that of your project, which can be changed in the Image Size dialogue (Control+Alt+I). So if you are creating something for display on the internet, it will ideally be 72 dpi, the resolution of monitors. If it is for print, it should be set to 300 dpi. The "Save for Web" is a convenient tool, but nothing that can't be done easily without.
On export the resulting slider (1-12) is just a measure of the relative quality of the file. The closer you approach 1, the smaller the file size, but also the more compressed the image is. The compression clusters like-colors together creating the artifacts around edges. If you don't want these, try switching to a format like PNG which does not compress your images.
9 Years of Web Design