Multi-Classing – Biggest Challenges and Best Classes for Mounted Builds?

My goal is to create a Kobold mounted fighter to be useful in a group of two bards, a sorcerer, a rogue, and a ranger. We start with level 2. I'm surprised if we go beyond Level 14, but it could happen.

Currently, I tend to these classes:

  • Cavalier fighter
  • Oath of the Old Paladin
  • Multi-class of the two

Question:

I understand the differences well on paper, but I wanted to know if anyone has experience playing mounted builds. If so, what were the biggest challenges you found?

How many times did your horse die? Was it ever a big problem to fall off your flying mount? Or was the biggest problem in rescuing rescue throws?

Another context

I want general feedback. But right now I'm trying to decide for the class.

Pally seems to be great, but it's a bit of MAD for a goblin wanting to get into a riding fight early.

My thought of a pally-dip was, even though it's a 2-level delay and 13 cha buy-in, with Fighter 5 / Pally 2 I get an extra fighting style, putting myself on my hands, occasionally placing punches or blessings, and casting or Cast Search Find a larger horse of scrolls (with the help of a Fortune Telling Assistant).

If we had gone all the way to 18, I would probably go Fighter 11, then Paladin 7. IF I dived in, which is a big jump.