The main characteristics of the classical symphony, as it existed by the end of the 18th century in the German-speaking world were:
4 movements, of which the first would usually be a fast movement in sonata form, the second a slow movement, the third either a minuet and trio or a ternary dance-like (scherzo) movement in "simple triple" metre, finishing with a fourth, fast movement in rondo and/or sonata form.
Instrumental, to be played by an orchestra of the relatively moderate size customary at the time.
After Beethoven started experimenting with the movement structure and with programmatic features in his Sixth Symphony, and later added singers to the last movement of his Ninth Symphony, the possibilities for moulding the symphony format appeared unlimited, starting from the early Romantic era, for example:
Extend the programmatic layer: even after the tone poem had split from the symphony genre as such, symphonies were published with extended programs, explicit (as in Berlioz' Roméo et Juliette, after Shakespeare, as well as in his Symphonie Fantastique) with clearly described literary/poetic devices (as in John Kenneth Graham's symphony cycle, or more implicit, like a succession of sentiments (as in Tchaikovsky's Sixth Symphony), Carl Nielsen's The Four Temperaments