Regarding the illumination/background correction: 1) while everything is optional, to be quantitative, this step really cannot be skipped. It might not be necessary quantification by counting (e.g. smFISH experiments), but it is absolutely necessary to ensure accurate quantification of fluorescence when performing experiments where fluorescence is being quantified.
Also, the most essential part of the method of illumination correction (also called flat-field correction) is by dividing by an image of uniform fluorescence, not subtraction. Backgound subtraction is essential as well, but that comes later. Figure 4 in Jennifer Waters' "Accuracy and precision in quantitative fluorescence microscopy" is a very helpful illustration, as well as description in the figure caption. "Quantitative Analysis of Digital Microscope Images" by Wolf et al is another great resource. [Interestingly, the tutorial linked to here "tutorial on the ImageJ website" describes the method correctly for brightfield imaging].
Here is a description of the image calculations from Wolf et al.
XVI. Exercise 5: Flatfield Correction
Take an image of the homogeneous (fluorescent) field. We will call this H(x,y).
Take a background image in a region of no fluorescence: BH(x,y).
Background correct homogeneous field image: H′(x,y) =H(x,y) −BH(x,y)
Take an image of your sample: I(x,y).
Take a background image in a region of no fluorescence: B1(x,y).
Background correct your image: I′(x,y) =I(x,y) −B1(x,y).
Perform that flatfield correction: F(x,y) =I′(x,y)/H′(x,y).
Importantly, even though the above steps include "background subtraction" it is still necessary to perform background subtraction of the flat-field corrected image. See Table II in Waters 2009 (http://jcb.rupress.org/content/185/7/1135#T2) for a summary of steps to follow in fluorescence microscopy imaging.
While some microscopes can automatically perform flat-field correction using saved reference images, practically speaking, this correction is best when done "fresh" for each experiment. During every experiment, prepare a blank position (for example, in live cell imaging, include a well with media only) that will provide uniform fluorescence (media with 10% FBS in my experience provides sufficient fluorescence from autofluorescence). You can collect images of this position of homogenous fluorescence (I usually take at least 5 images and compute a median image) and subsequently use this to divide images of your cells.