There have been at least 100 or more questions of this exact nature asked on this board since I have been on it, the answers are always the same. A search here for harvesting bow would tell you everything you need to know.
Cut any size tree you think you can handle, one 10" to 12" in diameter is much easier to handle than a 24" monster.
Harvesting bow wood is easy, cut white wood in the spring, split into staves 3" to 4" wide, peal the bark off, coat the ends and back with a sealant, I use shellac, and store the staves in a weather protected area out of the sun to cure. They will dry at a rate of 1" of thickness a year, trimming the staves down to bow blanks will greatly speed up the drying process.
You can cut white wood anytime but after mid summer the bark is very difficult to remove, save yourself some grief and cut your white wood in the spring.
For osage cut it anytime, the myth of having to cut it in the winter when the sap is down is prevalent, the time of year you cut it doesn't matter.
Split the staves, the bark and sapwood have to come off together or the sapwood will probably check if left on. If you choose to leave the bark on you better spray it with insecticide wood wasp lava or powder post beetles with go to work on your staves.
Like all green staves the ends and back have to be sealed for drying.
