Classical Music?

https://www.youtube.com/watch?v=ONxnzzD67Xs Kapustin Etude No. 6 definitely has a beat, really catchy too, perfect for teens who want to get into classical.

maybe something like chopin etude 25 11 ( around 20 seconds in things will really start happening) https://www.youtube.com/watch?v=lS9J2WAlN-0
Apassionata is pretty catchy
Moonlight sonata 3rd movement
Rachmaninoff's Red Riding hood
Stravinsky's piano concerto (around 1.30 things get interesting)
Liszt's La Campanella
my personal favourite: https://www.youtube.com/watch?v=AapjpeqmviM

Piano and violin? How about some Stravinsky - http://www.youtube.com/watch?v=uxI6CTW3eKQ

I'm not familiar with chamber, but I know a lot of piano pieces with a beat. For whatever, pieces influenced by Hungarian music tend to 'have a beat' as you say - especially Liszt's Hungarian Rhapsodies.

Brahms - Hungarian Dances
Liszt - Hungarian Rhapsodies 1-19 except 5 and 18
Bartok - Sonata (first and third movements), Allegro Barbaro. Sonatine, Six Dances in Bulgarian Rhythm, some of the Hungarian Peasant Songs,
Chopin - Some of the waltzes (Op 18 'Grande valse brillante', Op 34 No 1 and No 3, Op 42, Op 64 No 1 'Minute') and polonaises (Op 40 No 1 'Military', Op 44 'Tragic', Op 53 'Heroic', Grande Polonaise Brillante from Op 22, and a few others), Tarentelle
Beethoven - Sonata Op 31 No 3 'La chasse', Op 53 'Waldstein'
Prokofiev - Toccata, movements from some piano sonatas
Bach - many movements from the Partitas

Classical music can't be "super classical", it's either classical or it isn't.

Many people start with Vivaldi's four seasons. You'll probably enjoy this:
https://www.youtube.com/watch?v=-SUvnM3nqfU

There is no such thing as "super classical." Music is either classical or its not. Almost all of it has a beat, but probably not in the way you are thinking. In fact, if it has your kind of beat... it probably isn't classical at all. In which case you want the pop category.

So This Is Heaven by Sakis Gouzonis.
Santorini by Yanni.

Beethoven:

Symphony 5
Symphony 9
Piano Concerto 5

Brahms:

Symphony 4
Piano Concerto 2
Hungarian Dance 2

Tchaikovsky:

1812 Overture
Symphony 6
Piano Concerto 1

Schubert:

Symphony 9
Piano Trio 2
String Quartet 14

Schumann:

Violin Concerto
Symphony 1
Piano Quintet
Piano Concerto

Rachmaninoff:

Piano Concerto 3

You might be looking for what we call new age music. The Piano Guys are a GREAT example of that. It's kind of a mix between classical and pop (pop music played on classical instruments in a classical style). I like it, but then again I can't even begin to listen to today's pop so I'm probably not the best source XD try groups like the Piano Guys or Lindsey Stirling. This genre can be a great transition from pop into classical, if that's what you're looking for. Also, if you want a beat or percussive sounding classical music, try Edvard Grieg's music. Any of the Russian five are good too (Tchaikovsky, Prokofiev, Stravinsky, Shostakovich, and Rachmaninoff). In classical music, almost all stylistic markings are in Italian; the percussive style is marcato. Google something like "good marcato classical music" or something along those lines to find rhythmic selections. You might also look at jazz, it's pretty groovy XD

Say something- A great big world ft. christina aguilera.
I was there- taylor swift
The forgotten- Green day