Traveling to London in Mid April. Overwhelmed to say the least!

I’m heading to London in mid-April and feeling a bit overwhelmed! We’ll be staying at the south bank near Westminster Bridge with my two boys, aged 12 and 9. We’re trying to organize our itinerary by clustering activities in specific areas.
I’d love some advice on the best transportation options for first timers, especially for trips beyond walking, like getting from Westminster Bridge to the Natural History Museum. We’ve heard about the tube and hop-on/hop-off buses. Any tips on what else we should be prepared for would be really helpful!
Additionally, what should we expect in terms of weather and what kind of clothing should we bring?
Lastly, we’re planning a day trip to Paris via the Eurostar. How complicated is that process? Thank you in advance for any guidance!
That sounds like an exciting trip! Here are some tips to help you navigate London and make the most of your time there:
Transportation
Oyster Card or Contactless Payment: For travel on the Tube and buses, consider getting an Oyster card or using contactless payment with a debit/credit card. They’re convenient and offer the best fares. You can pick up an Oyster card at the airport or any Tube station.
Tube: The London Underground (Tube) is usually the fastest way to get around. To get from Westminster Bridge to the Natural History Museum, you can walk to Westminster Tube station, take the Jubilee Line to Westminster, then transfer to the Circle or District Line from Westminster to South Kensington. The museum is a short walk from the station.
Buses: Hop on/hop off buses are a fun way to see the sights, especially for kids. It’s a good idea to check if any bus routes conveniently connect to places on your itinerary.
Walking: Since you’re staying near Westminster, many attractions are within walking distance. Consider mapping out a walking route that includes sights you want to see along the way, like the London Eye or Big Ben.
Weather and Dress
Eurostar to Paris
Additional Tips
I hope you have an amazing trip! Enjoy your London adventure and your day in Paris!