Try to imagine the buildings full of marble and the statues with their heads. Think of the streets filled with toga-clad ancient Romans, discoursing on the progress of the Punic Wars, or going full fangirl over Virgil.
All in a long way of saying: yes, the forum is a bit crowded, even in low season. But the forum is also huge, so people are quite spread out.
WEAR STURDY SHOES. I would strongly suggest not wearing flip-flops. Strongly.
That Italian sun can get hot, hot, hot. Bring a water bottle (or a few) with you and a hat if you're sensitive to the sun.
Be sure to have a good map handy to help you identify buildings whose use isn't immediately apparent.
You can buy your tickets online, though expect somewhat of a wait when entering through the Colosseum, as we did.