If you're planning on taking the Circle Train from start to finish, it's worth packing a few snacks and maybe a toy or two for the kids in case they get restless.
The ride on the Circle Train from start to finish is about three hours long, so you might not want to stay on the whole time. Also, adults will need to have their shoulders and knees covered to enter the pagoda, so ensure you dress appropriately. If you forget, you can always rent a sarong at the pagoda.
It's best to ride the Circle Train in the morning, and see the pagoda at sunset. You likely won't be able to combine both (that would make it a long day), so decide which is more important. Personally, I'd rather ride the train later and see the pagoda at sunset. If you're able, try to visit on a Sunday. Every Sunday evening, there's a performance in People's Park after sunset the kids will love.
Yangon is great to visit any time of year, but fall, winter and spring are the best. The summer months can get very hot and quite rainy in Myanmar. It's best to avoid this time of year, if possible. The rain is typically sporadic though, so if you have to visit during the summer, just make the most of it.
Yangon is an incredibly inexpensive city, so just enjoy it.