Yes, I think that is a good shortlist - I would say as a rough guide, someone needs to have pretty much everything on that list, because any absence of those things is a red flag in itself.
The only thing I'd probably disagree with is "trying to make things better for you" - that's a tricky one, small gestures intended to make your life easier/nicer/etc are good, if they are intrusive or border on "fixing you" or doing things for you rather than supporting you to do them yourself, potentially this could be a red flag, if these "gestures" end up making you feel dependent on them. Certainly there should be no big, life-changing kind of "saving" gestures in the early days.
So, they need to have all of those things, and no red flags of the other less-obvious ones such as:
Signs of addictive behaviour
Badmouthing others
Signs of aggression in personality (including aggressive driving)
Sexism/racism/homophobia/any other kind of prejudice
Anything which makes you feel uncomfortable or uneasy, even for a moment
"Issues" from childhood or past relationships (I know this is one people, including me, struggle with because it seems unfair to judge on something such as this, but really any issues should be dealt with before getting into a relationship, because otherwise they WILL cause issues within the relationship.)
If there are ANY red flags there, including absence of the points made by teacup, it negates all the good stuff, because it indicates that their mindset is not as "good" as you previously thought. If you've always made allowances or given people the benefit of the doubt, it's really hard to let go of this, especially when they are excellent in all ways BUT one, but you have to be ultra cautious, especially when you have DC. Don't feel sorry for someone or feel you should give them a chance, if they have issues to deal with then they need to go away and deal with them first.
I think also it's worth bearing in mind that even if someone ticks every box on the list and seems perfect in every way on paper, it's still okay to say "No thanks" if they don't seem right for you in some way. Don't hold on to the belief that a "good man" is a rare thing and if you find one you must hold on at all costs, if you managed to attract one who was nice, trust me there are many many more out there :) Expect the best, and you'll only put up with the best and you'll be happier for it.