Something I found interesting: The Marcello sonatas are not marked with beats-per-minute but with the Italian tempo names. Some movements are written in 4/4, but the "pulse" is on the 8th notes, so, for example, "Largo" translated to BPM refers to 8th notes, not to quarter notes.
Yes, this is very true - what you have to remember is that the tempo is for *the accompanying instrument*. They are the ones playing "Adagio, or "Allegro". This means that many of these tempos are (theoretically, anyways) much faster, or much slower, than bassists currently play them.
This is only a recording that I made for reference for myself, so it's not exactly my greatest playing, but it shows how the first movement of Marcello's Op.1 no.2 in E minor/G major sounds when the accompaniment part plays Adagio, instead of "molto lugubrioso" as we often hear it. "Adagio" is just a smooshing together of "ad agio", which means "at ease", and this accompaniment speed is certainly easier to play (though makes the upper part more sprightly).
Pretty different, right?
Largo = broadly
I agree that often the metronome markings are in conflict with the tempo headings, whether it is the composer, editor or just common practice. Beethoven music is often given as an example. Some say that his metronome was faulty (fake news ?) Myself, I think of Moderato being around MM 80 - 92, Allegro moderato about 110, Allegro 120+, Presto 144, Prestissimo ............(every man for himself !!!)
Definitely fake news, but they might have also been "aspirational" tempi, especially as you get into his later music when his deafness became more profound. Sometimes composers just want things that feel unachievable - Nielsen's tempi and bass parts come to mind.
Learning what the terms actually mean - ad agio meaning 'at ease', allegro coming from allegria, meaning 'happy', is important, because it's going to give you context about what the music should feel like, as well as speed.
my "order of operations" for more modern music (late classical and forward, depending on how you define the classical era), is thus:
1.) Look for a metronome marking.
if that seems weird, or is absent altogether
2.) ask the conductor, or
3.) ask the concertmaster depending on who's available.
if you're doing solo music,
4.) use the tempo word to approximate a reasonable tempo that sounds good on the instrument you're using.
For anything earlier than that I discard metronome markings entirely. they're all editorial and not given by the composer - meaning, they're as much hot wind from a horse's behind. You can use them as an indicator, but they likely stink. Composers occasionally wrote down their preferences (like Quantz). Performers will have their own preferences, and so will teachers. Editors make arbitrary decisions, or have their own preferences, even on urtext editions.
It's maddening if you think too hard about it.
Find a tempo you like that makes sense, and that you have made an informed opinion on. Someone's going to disagree with you no matter what you do!