You must like walking up hills.
We were there in July and as predicted, it was hot. April should be better in that respect.
We slept the night on the wall at Jinshangling and then walked to Simatai. Awesome !! Apart from the ever-present hawkers, being on the wall (nearly) on your own is great and well worth doing.
I don't know that I'd want to spend all that time trekking on the wall, but that's me. There is so much else to see, do and experience in Beijing/China.
I took a 40D, 50 1.8, 17-85, 70-300, 580EX and a Manfrotto 190XProB in/on a Kata 3n1-20. I don't think I'd have missed the 70-300 or the flash. I took all that on the wall. Get a bag/pack that carries plenty of water.
Other than the wall, be aware that it will be hard to get good shots of the tourist sights unless you can get there very early. There's more than 2 billion Chinese and it seems like they all want to go to the Forbidden City on the same day as you.
Steve.