Is the Express train worth it, how is Uber like?

My flight will be coming in at 3pm on a weekday, I guess it might take 1 hour to clear customs, and another hour to exit the airport and reach london, so it might be ~5pm then.

I guess I will have 2-3 hours to explore around, and at that time most will be closed.

Is it worth it to go to Windsor Castle, or Big Ben, or Buckingham Palace? Any other things or thoughts? Most all of these close at 5:00pm so no time.

Also, will it be OK to walk around with a carry on luggage with wheels?

Thanks!