Things I must remember about DMing the home game

I've been trying to figure out what feels wrong when I'm DMing the home game, and I've got 2 conclusions.

1. The degree to which I make things up on the fly makes me feel responsible for their outcome, and worry that they aren't fair. Thus, I fudge in the party's favor, which they usually pick up on. They have commented more than once that "If that's what happens, it happens," when a character's about to maybe die and I'm waffling about numbers or dice. THIS IS BAD.

2. While C&C is close enough to 3ed to be comfortable for the players to play, it is not a good fit for me as a DM. Too fiddly, too badly edited, and the math doesn't line up with my 2e and Mentzer background in a few important spots so I feel less confident about improvisation.

Here's what I need to do:

1. Prepare more in advance, but efficiently so that if they do something unexpected I have many scenarios ready. Figure out the minimal amount to prepare so that I am confident it is fair and don't appear to be making anything up on the fly, but can be totally impartial. I need to move away from such a narrative style or unwanted fan service and towards a Zak or Jeff model. It is not "the story of these characters" but "the game these players are playing and the story we are collaboratively telling."

2. Figure out the best system to switch to on my side of the DM screen. Have them keep C&C characters, or convert to hacked 3e. Work out more explicitly how ability checks and combat work so I'm not making it up new every time in the moment.

I am good at making shit up on the fly, but the degree to which I'm doing it is working against me. Everyone seems happy with the game and my DMing so far, but they don't exhibit a lot of tension.  I haven't been able to enjoy it as much as I should be. Time to fix that.