What’s the best ratio of half and half to heavy cream for homemade ice cream?

Yep go with about a 2:1 and you should be fine. I do closer to 1:1 but again that's how I like it. Too rich. The ice cream will feel very oily in your mouth if you go past 25% or so.

I use 1.5 cups whole milk, 1.5 cups heavy cream or 3 cups half and half, to 3/4 cup sugar and 5 egg yolks.

I'd go 60/40. 60 half n half to 40 heavy cream. But ultimately, it just takes practice. 

I used to make fat free/sugar free ice cream with fat-free half and half, you need to add some guar and xanthan gum for the improved mouth feel but it worked and was pretty good for the number of carbs and fat.  I find the ice-maker owner manuals to have the best recipes. Follow one of those and adjust to your preference after getting a baseline.

Add a bit of Booze to the recipe that uses more half and half. The alcohol will keep it a bit softer. Just a few tablespoons should be enough.

Few ideas for you.

Chocolate and amaretto (that also pairs well with fruits like cherry, peach, apricot and raspberry as well as almond and most other nuts. 

You can use Kahlua with coffee ice cream, chocolate as well as any you might mix nuts in with. 

Limoncello with vanilla, lemon, raspberry