hundred of different opinions.
but this is what i would do- choose the better cleaner side- and possibly the tension side- if both were equally clean, then split it in half, make the tension side into staves, and saw the other up into blanks for lams.
i always like to mark which is top and which is bottom when cutting a branch- so the tension and compression sides are clearly distinguished. dont mix them into the same board, other wise you will have increased movement in the wood when drying.
unless of course it is a straight up and down branch- then i would be looking to see if the heart is on center, and then if it is off center, treat the "thinner" side as the stave material- it will be denser, and it would be wasted on lams, and be better for staves.
cut them a bit oversize, and seal the ends, then sticker them in a cool, wind free place, until equilibrium mc is reached, then you can chase the moisture a bit-
when you sticker and stack them, put a weight on the top to help stop the top boards from warping.
i would cut them into 2 x 2 's that would give me the option to use them in either direction, and would facilitate quicker drying.
you can build a very simple kiln too, with some builders plastic, a de humidifier and after a while a light bulb or two for heat- but not until the high mc has dropped a bit- rush the moisture out early on, you run the risk of case hardening the wood, and also checking it like crazy.
the knotty side will make for prettier lams too.
thats just how i do my re sawing on my logs.
there are some good u tube videos to make a plywood sled in order to resaw accurately on your bandsaw- will see if i can find one.