A number of rules are standard for hyphenation with full-justified margins. The short answer is that you should never end up with -es when splitting lines, but segments of three letters or more are possible. My advice is mostly to ignore the effect of the plural on the word.
Guidelines may vary from house to house. Here is one example from the Handbook of Technical Writing, 12th ed., "hyphen" (p.239):
Hyphens are also used to divide words at the end of a line, especially for full-justified margins within small columns. The following are standard guidelines for using hyphens to divide words at the end of lines:
Do not divide one-syllable words.
Divide words at syllable breaks, which you can determine with a dictionary.
Do not divide a word if only one letter would remain at the end of a line or if fewer than three letters would start a new line.
Do not divide a word at the end of a page; carry the word over to the next page.
If a word already has a hyphen in its spelling, divide the word at the existing hyphen.
Do not use a hyphen to break a URL or an e-mail address at the end of a line.
The first three bullet points are essential. No, you don't break up one syllable words. Yes, you can determine syllabification with a dictionary. No, you don't leave a two-letter segment at the start of the next line. Combined, these adjudicate examples like appliance:
Pick a dictionary you'll use consistently (here I'll use Merriam-Webster; for your purposes pick whichever you feel is consistent and in line with your purposes)
Observe the syllabic breakdown of the singular form (ap·pli·ance)
Break at a point that leaves at least three letters at the end and more than one letter at the start (ap-pliance or appli-ance)
One other guideline could help you choose between the two options. If you have a choice, it's practical to include enough of the word to provide clues as to pronunciation and thus what the resulting word will be. (Editor Andy Hollandbeck puts it like this: "A reader should intuitively understand how to pronounce the first part of a broken word without knowing the rest of the word.") ap- could end in apiary or appliance, which would change the a a lot, so appli- gives more information on how to pronounce the resulting word.
What would change with the plural form? Here, you need change nothing. You already have one or two acceptable break points, so making a decision on the plural is unnecessary. Appli-ances is fine. For most words, the "s" doesn't make a meaningful change, especially if the word is longer than two syllables. You will already have viable options.
If you adopted this measure, then though fences is two syllables and could theoretically be broken up in accord with the previous rules (fen·ces), because the singular word is one syllable and wouldn't be broken up, you can decide not to break it up either. (Is one character truly that crucial?)
The possible exceptions to these rules are rare, but crop up with two-syllable words where the plural form results in a three-syllable word. With a word like cadence (ca·dence), the plural (ca·den·ces) invites a possible choice between guidelines. Do you go with the break-down that gives more information about the pronunciation of vowels (since for ca- the result can involve a soft or hard a), or do you stick with ca- because it is in line with other guidelines in the singular? The latter is simpler, but the former gives you slightly more flexibility.