The notion of “most typical tone lnguage” can be understood in terms of specific properties that are most typically encountered in tone systems (not counting the number of speakers of each language, as a way to get Chinese languages to be “most typical”). This does include so-called pitch-accent languages because very many tone systems have been labeled pitch-accent languages, for example Luganda has been said to have such a system, based on the property of restricted distribution. The Ibukijima dialect of Japanese looks on the surface like as contour-dense West African language, yet it is analyzed as a pitch accent language. The matter of Norwegian and Swedish tone is a bit more complex, since it sort of seems to be completely predictable, just not surface predictable, so I will exclude Scandinavian.
One question is what is the typical number of levels: either 2 or 3, I’d wait for a major statistical survey to decide that. Chinese languages seem to be amenable to description in such terms, though traditionally tones are actually treated as having 5 different levels, hence the analysis in terms of 45, 31 etc. which is over-phonologization of perceived differences (generative practicioners like Yip have been countering that tendency).
The second question is what the density and structure of contours is. Most typically, the contours in a tone language are a proper subset of the two-level combinations of contrastive levels. So in a 2-level system, there may be two contours, rise and fall (theoretically, you could have 5 kinds of rise and fall but only two level tones – and I think you do in some Chinese languages, for example only 1 level tone in Mandarin and 3 contours). Two-level systems that exploit the maximum of two-endpoint contours (2) are not as common as ones that only allow fall as an underlying contour (and the typical single contour is fall, not rise). Looking at three-level systems, the pattern is more noticeable, that it is hard to find a language with 3 levels and 6 underlying contours. It is not clear to me whether completely contour-free languages are the most common type, but this brings us to more general restrictions on contours. A final point about contours is that they typically only involve two endpoints, and three-point complex tones (rise-fall) are quite rare.
Typically, there is a substantial distributional asymmetry between level tones and contours: any syllable can be H or L (or M), but contours are often restricted either to final position, or to certain syllable types (heavy ~ long vowel). Even factoring out the limited distribution of contours, full exploitation of all possible tone patterns (T^n – number of tones T raised to the power of the number of syllables n) is uncommon, once n goes over 2. The theme that I’m pointing to here is that tones are typically not distributed very densely, given the theoretical potential of specifying each and every syllable with a distinctive tone.
The non-density of underlying tonal contrast is what is mostly behind the scandalous notion of “pitch accent”. This concept is based on an analogy to typical stress systems. Typically (English being atypical), stress is on some single syllable of the word. (Secondary stress complicates the matter a bit more, so you have a single primary stress and then some system of alternating secondary stresses, in the typical case). A tone system with a single tone specification per word / morpheme thus has some similarity to stress systems, except that typical stress systems do not arbitrarily specify location of stress in the lexicon (again, English is not typical), instead there is some system of rules determing where that stress is. Whereas in restricted tone systems (such as Luganda or Japanese), you still have to lexically specify where the prosodic contrast is in the lexicon.
Chinese languages have two striking properies that are rare in other tone systems. One is the “unit contour” property. The standard autosegmental deconstruction of contours as combinations of L, H on a single vowel is challenged by some examples in Chinese languages where contour tones seems to spread as units (the Danyang case). The second is the arbitrary-sandhi property where tone changes are most efficiently described by numbering the tones (1, 2, 3, 5) then giving a table of replacements (1→3, 2→7…), rather than decomposing tonal alternations into phonological simple phonetically-based operations like “spread H to the left”, “delete L before H”.
In a nutshell, I would say that the typical tone system is not “dense” in the way that Chinese or Vietnamese are. Instead, they are sparse, as Korean, Japanese, Bantu, tonal Indic, Tibeto-Burman, Cheyenne, New Guinean or Western Amazonian languages. Discerning what constitutes “typical” is a very difficult research project, which has been hampered by lack of descriptive material (a lacuna being slowly filled over the years).
I propose that the best way to look at these questions is not in terms of Chinese vs. the rest of the world, instead it is in terms of fundamental monosyllabism vs. longer words. The characteristics of Chinese are also found in Grassfields Bantu, Vietnamese, Taa (Khoisan), Kru, and in general are not so rare when words are typically monosyllabic.
I will think about whether there is some one language that strikes me as most typical, but a first-impression candidate is Igbo.