It sounds like you are looking for halter style and the good mind for an all around horse. There are quite a few lines that have that. The good mind part is what makes it a little more intricate. That's not the kind of thing you can see on paper, but learn by talking to others and dealing with the horses themselves.
There are two routes you could take with breeding your mare. They would each involve different lines.
PM if you would like detailed info. I don't want to make it seem like I'm knocking someone's lines. They all have their own purpose, but some have a few more advantages than others.
@Standards Equine Good point however interestingly enough, I put disposition before conformation now, without sacrificing either of course. And I believe it is 99% genetic. So I know what lines have good minds and which ones are simply crazy. Especially with buying babies or broodmares, I find handling doesn't affect their natural dispositions, unless it's extreme e.g. heavily spoiled or abused. But I have bought so many horses sight unseen, sometimes even without more than a headshot now, from my chosen lines and had them all be just as sweet and easy as could be. No more crazies here and it's a wonderful thing! Lol