Beginner Movement - Mario cam on entry and delay the C-Down to make sure your camera is directly behind you.
Intermediate Movement - These options are for intermediate players and above. Which you chose is a matter of preference. Both begin with a C-Left followed by Mario Cam and C-Down. Hold A before after the camera inputs to allow you to buffer a kick once you have control of mario. For the Mario Cam option, stay in Mario cam the whole time while pressing C-Right to adjust the camera. For the Lakitu Cam version, switch to Lakitu Cam during the first long jump, then input one C-Right when you land.
Beginner
Intermediate Mario Cam
Intermediate Lakitu Cam
Lava Boost
As you can see, there are many options for the lava boost portion of the star. The easiest and safest is the Triple Jump Boost, however it's quite a bit slower than all other options. The remaining options are all fairly similar, with timesave scaling well with difficulty. For most players, the trade off between difficulty and time save with strat selection is a matter of preference.
Similarly to the lava boost section, there are many different ending movements you can perform for this star, with varying levels of difficulty and timesave. Depending on the type of boost you choose, certain ending movements may become easier or harder. The video below goes over each of the endings, how much time they save and roughly how difficulty they are.