Not much info. But I would start looking at "modern" in the sense of "didone" typefaces...

Look for something where classic lettershapes have been given a neat, clean, reductive finish.
I've done that in a few faces, such as Beaufort (apparently a cheese as well) and Bodoni Egyptian.

Alright I think first I need to make sure that I understand you.

"mondern" can have different meanings. From the perspective of philosophy, history and social sciences it would describe the Age or Reason and Rationalism, form the enlightenment onwards, and traces can be found in the way people think up to the 1960s. (Some actually argue, that the deathly system of the Nazis was rationalism in extreme, Adorno for example) Generally speeking you can summarize the "long" 19th century as the main time of modernity.

As people here are familiar with history of ideas, you got two answers so far, which interpreted your "modern" as "19th century type". Giving you answers related to the Didone types and other modern typefaces.

I assume you mean "contemporary".

With classical I guess you refer to something like "traditional", "old-school" and "established"? This would be probably every mainstream text typeface from the renaissance, to old style, to then actually modern(!) (Scotch, Didone, Bodoni) and Transitional.

Based on the assumption that you want a contemporary but still traditional typeface, I would recommend you:

Some more rare:
Maiola
FF Yoga
FF Tisa
Linare
Relato
Fresco
Stuart
Adriane
Enigma

Enschedé Font Foundry has some gems

The usual suspects - for a good reason:
Whitman
Freight
Swift
Mercury
Prensa
Expo Serif
farnham
Warnock

More in the traditional corner:
Girande
Borges
Galliard
Malabar
Leksa

I guess this list is a good start.

Although if you actually meant a modern kind of typeface (19th century) in a contemporary reinterpretation, then I think Nick Shinn is quite the expert here. With the mentioned Bodoni Egyptian and his

Scotch Modern.

You might then like as well:

Miller
Ingeborg
Escrow

Alright, I hope this will give you something to work with ;)

best

Thanks so much guys, my day just got a lot better =D !!

I guess with my extensive list I killed all further discussion in this thread. Which one will it be in the end?

Someone asks for a “classic modern” (or was it ‘modern classic’?) – and we don’t realise what she is actually looking for.

– Why?

Because we lack an appropriate terminology to accurately describe a face’s characteristic. This is really a mess: for type users who can’t quite find what they look for; for type providers who have no tool to market fonts precisely.

Has anyone a clue about what has been achieved in type classification so far?