Best time to go to Italy???

Okay need some advice...

We’re planning a trip to Italy and wanna do Amalfi Coast and Rome. The main thing we’re excited for is Amalfi....like beach clubs, swimming, boat rides, all of that. But we also wanna spend some time in Rome and explore.

At first I was like obviously summer… but now I keep seeing people say August is insanely hot and “unbearable”.

I don’t mind heat if we’re at the water, but I’m more worried about Rome and walking around all day in the heat. Is it actually that bad or are people being dramatic??

We're looking at September but it looks more expensive, and I’ve seen mixed things about the weather. October seems cooler which sounds nice for Rome, but I feel like it might take away from the whole Amalfi beach vibe.

However, if September really IS the best month to go, we will go with September. Just trying to see if it's absolutely necessary to spend the extra $$$ to go that month.

So basically:

• is August actually miserable or still worth it?
• does Amalfi feel fine since you’re by the water?
• what would you pick between August, September, or early October?

Where we're from we're used to warm weather, just not the crazy humidity.

any advice or experiences would help!!!