Naming the spin system present in ethyl butanoate
By Pople Nomenclature convention, coupled nuclei for which the chemical shift difference is much greater than the coupling between them (say, greater than 3-5 times) are labelled with letters alphabetically well separated (AX, AM etc). Labelling nuclei with adjacent letters of the alphabet (AB, MN, XY etc) indicates that the chemical shifts are close compared to their coupling, and this means they are typically strongly coupled ie cannot easily be analysed using first order techniques.
As for so many NMR related questions on this site, I refer you to Hans Reich's valuable online resource for further reading. 

So, what to call your system. Clearly, this is an example for teaching purposes only. You have correctly identified that you have 5 non-equivalent sites with relative populations 3:2:2:2:3. If you cannot work out, or do not know what the expected approximate chemical shifts would be for each of these guys I can tell you they are well enough separated not to worry about second order coupling. 

So now you need to do is determine whether you have any magnetic inequivalence in your system. Again, have a read of this useful page to understand how to test for this, but I think you are fairly safe with this case that there are no nasty surprises.

All that is left is to assign your spin labels to your system. So for the propyl group, none of the chemical shifts are close (compared to coupling) so your labels should be well separated; so not ABC, but something like AJM. Likewise for the ethyl chain; something like RX. I'll leave you to work out how to put the two together.