Hi! I remember you from before! Glad to hear you are getting back into chickens maybe!! I have taken chicken breaks before as well.
My Black Australorps and LF Easter Eggers don't fly over my 5 foot high fence section. However, they will land on the
gate's 5 foot section and then fly out, so I had to add some height to the gate. It was because there was a convenient pole across the top to rest on.
"Heavy brown egglayers" are good. If your fence is less than 5 feet high they may fly out. Even my Buff Orps flew out over 4 feet high fencing back when I had them.
The Mediterranean breeds are better fliers. MUCH better fliers. As in, they are up in the trees. So I don't recommend them.
It sounds like you aren't interested in bantams. Some of the bantams fly quite well and others not at all.
I hope this helps and do try to get all your chickens at once if possible so they all get along in the best possible manner. Sorry if I am telling you stuff you already know LOL.
One thing I can tell you is that my Black Australorps and EEs tend to be pretty gentle but EEs can be flighty and standoffish
or friendly- and my EEs tend to be near the bottom of the pecking order when combined with more aggressive chicken breeds. My favorite friendliest chicken right now is an EE.
https://www.mcmurrayhatchery.com/heavy_breeds.html?cl=crumbtrail
http://www.idealpoultry.com/pdf/retail_breed_description-2014.pdf
