One transition I recommend would be the match cut.
It's not flashy; that's kind of the point. Done well, nobody registers that a cut even happened. No wipe, no dissolve. The cut does all the work on its own.
It's also one of the more approachable places to start. The simplest...
Everybody needs a fun weather app. Introducing the best weatherman, Pip.
Pip is a round, jelly-soft little creature who takes the forecast personally. Sunny? Shades on. Rainy? Umbrella up. Stormy? Gripping a lamppost for dear life. Night? Barely awake, glowing softly in the dark.