In English for example, the "ch" sound (as in China) is sometimes written as /t͡ʃ/, other times as /ʧ/ or simply as /tʃ/. Similarly, I have seen the German "tz" (e.g. Katze) transcribed as /t͡s/, /ʦ/ and /ts/.
Is there an "official" recommendation on which option should be considered correct?
"tʃ", "t͡ʃ", and "t͜ʃ" are the only representations of the affricate currently sanctioned by the International Phonetic Association. The ligature symbols "ʧ", "ʦ", etc. were removed from the alphabet at the 1989 Kiel Convention.
The arches in "t͡ʃ, t͜ʃ" are called tie bars. Note the IPA chart says "Affricates and double articulations can be represented by two symbols joined by a tie bar if necessary" (emphasis added). They are essential in languages where an affricate phoneme and a homorganic stop–fricative sequence frequently contrast, such as Polish, but otherwise they are omitted more often than not. I do not know of any dictionary of English or German that makes use of them.
In theory, the difference between /t͡ʃ/ with a tiebar and /tʃ/ without is that the former represents a single unit and the latter represents two units. This is sometimes important for theoretical reasons (you might want to treat /t͡ʃ/ as a unit because it lets you make some phonological generalizations) and more rarely for practical ones (Polish contrasts affricates against stop-fricative clusters: /ˈt͡ʂɨsta/ "clean", /ˈtʂɨsta/ "300").
In practice, most people don't bother to write the tie bar unless it's important (as in Polish). So I've seen both /t͡ʃ/ and /tʃ/ in different transcriptions of English, without any meaningful implication.
/ʧ/, the single character, is obsolete and no longer part of the IPA. But it would mean the same thing as /t͡ʃ/ with a tie bar: a single affricate unit rather than a stop followed by a fricative.
The 2015 IPA chart is freely available from the Association's website. It does not include affricate characters in the form of ligatures (such as ʧ and ʦ); it does include a note stating "Affricates and double articulations can be represented by two symbols joined by a tie bar if necessary", giving the examples "t͜s" and "k͡p". The implication is that if not necessary, affricates and double articulations may be represented by two symbols in sequence without a tie bar, like your examples of ts and tʃ.
There may be more detail in the 1999 Handbook; since it is not free, I have not read it. Wikipedia states without a source that the ligatures for affricates "are no longer standard IPA".
