Pieces like Beethoven's 5th Symphony have been described to me (by conductors) as "notoriously difficult." So what do they start beginners on? And what makes certain pieces more challenging than others for conductors?
Beethoven 5 is tricky for conductors in the first handful of bars (the very famous bit). It's because of the abrupt pauses combined with the fact that the big 4 note motto starts each time on an offbeat, after a quaver rest. Also, it's in a quick 2/4. They must decide to conduct in a quick 2 or slower 1. That's a lot to handle for an inexperienced conductor, and if he/she is unsure at all then the orchestra will certainly feel it too.
Beginners would do better to start with something that behaves itself more. Something that starts on the beat and flows in regular phrases would be good. For example, Haydn's Surprise Symphony, 2nd movement (Andante).
Many things can make life difficult for conductors. For example - rhythmically unusual or unstable passages - when the orchestra is being brought back in after say a soloist's cadenza can on occasion be a bit hit and miss - when enormous forces are being conducted and held together by one person (large orchestra and choir, plus soloists), and so on.
Beethoven 5 presents no problems to a 'commercial' conductor who is happy to give a clear 'and ONE' in front of 'Da Da Da Daa..' The classical guys sometimes feel it's infra dig to 'count in', and tie themselves up in knots.
There's a similar situation at the opening of Mozart's Magic Flute overture. You can give two clear preparatory beats to the semiquaver pickups, or you can get all artistic and try to do it 'on the nose'.
This goes some way to explaining why the classical world tolerates instances of sloppy ensemble that would get a Broadway musical director fired.
There's stick technique and there's artistic concept. To teach the first, I might BEGIN with Beethoven 5.
Have a look at this video to see what young conductors find difficult
A search for 'conductor cam' can also be illuminating - here are two styles of theatre conducting.
It would make sense for beginning concert band conductors to be started on Grade 0.5-1.5 concert band pieces. I've found that those pieces tend to have dirt-common time signatures (4/4, 3/4, 2/4, maybe 6/8), constant and relatively moderate tempos, and conservative key signatures (invariably Bb major, G minor, Eb major, C minor, F major, or D minor--note that many concert band instruments are Bb/Eb/F transposing instruments, so C major is often too difficult).
Meter changes and tempo changes are invariably going to make pieces harder to conduct. 5/4 and 7/8 are also trickier time signatures to conduct in. Extremely slow music may still be reasonably easy to conduct, but extremely fast music won't (due to the hand movement speeds required).
And then there's the conductor's desire and ability to convey changes in dynamics to the players, which can definitely make pieces even more difficult to conduct.
I believe a lot of the same principles of what makes pieces easy to conduct apply to orchestral conductors.
Conducting is not just waving a baton up and down with a steady beat, this can be done with marching music because there is a steady 1,2,1,2...
As soon as you have a polyphonic piece with instruments entering and dropping out at critical moments, the conductor has to look at the player and give them a nod at the right moment. The sound levels also have to vary between different sections of the orchestra. The conductor may want the brass to play softly and the strings loudly or vice-versa. This is indicated by hand gestures whilst looking in the correct direction.
For this reason the conductor has the know the whole of the score intimately and have their own idea of exactly what should sound how.
Apart from interpreting the score, the conductor's role is to keep everyone together. It is almost impossible for a large orchestra to keep in time without a conductor - this is partly due to the speed of sound so if two players are separated by a distance they will both tend to slow down in order to match each other.