For Classical Latin, I have never seen any pronunciation given for <NG> aside from a nasal consonant followed by a voiced plosive. I would assume the reason /ŋ:/ is used in Finland is simply because that's how "ng" is pronounced in Finnish.
For example, a word like pango has the reconstructed Classical Latin pronunciation [ˈpaŋɡoː].
Classical Latin did not have a phonemic distinction between velar and palatal plosives. Words like gingiva are analyzed as containing the phoneme /g/, but it's likely that in this kind of context, the voiced plosive transcribed as /g/ was phonetically fronter than the /g/ in a word like pango. So it's possible that the phonetic form of a word like gingiva might have been something like [g̟iŋ̟ˈg̟iːwa] or [ɟiɲˈɟiːwa]. However, allophonic fronting of velar plosive phonemes next to front vowels is often not transcribed even in phonetic transcriptions, because to speakers of languages like English and French the front quality of a plosive in this context is not perceptually salient.
Classical Latin is also usually analyzed as lacking a velar nasal phoneme, so strictly speaking there is no /ŋ/ here or in any Latin word. In this context, sounds like [ŋ], [ŋ̟] and [ɲ] did not contrast with [n], so the usual phonemic analysis of the cluster is /ng/. Some phonological analyses make use of entities known as an "archiphonemes" to account for lack of contrast in certain specific contexts; if we use the symbol |N| to represent a nasal "archiphoneme" in Latin, we might instead say that the phonological form of the cluster is |Ng|.
the case of "-ngu-"
The situation is basically the same for non-syllabic <NGU> in words like lingua, although there are some arguments about the phonemic analysis of non-syllabic <GU> and the allophony may have worked a bit differently.
In theory, we could analyze such words as containing a unitary phoneme /gʷ/. Allen (Vox Latina) somewhat hesitantly endorses such an analysis, by analogy with voiceless /kʷ/, for which it is easier to make a case for a single-phoneme analysis (p. 25). However, I believe most linguists prefer to analyze Latin non-syllabic <GU> as a cluster /gw/, on the grounds that a phoneme /gʷ/ would have an unusually highly restricted distribution (when not preceded by <N>, <GU> is always syllabic /gu/).
Allophonic palatalization may also have worked a bit differently for words with <NGU>. Allen cites a passage in Priscian in support of the proposition that the labial element represented by <U> in <QU> and <NGU> may have had a front articulation before a front vowel (p. 17).