Ah, I know Palatka. Pretty part of the St Johns there, I did a little kayak trip there once. Net some nice shrimp right off of docks there at times. You've got all the power you need to run any kind of 24" bar without blinking w that 592xp, so you could run regular 3/8 fine but I think you'd get better results with .325 .050 chain. I'm sure Oregon or Husky makes one, but finding the right one w the mount for your saw that's solid steel instead of laminated in that size isn't as easy as it could be. If you want to keep it simple and not have to change out your drive sprocket, probably best to stick w 3/8" that your saw came with so you can switch back to your 36" bar for other sawing.
Oregon 240RNDD009 Powercut bar is a solid body 24" bar for your saw, 3/8 .050. Then you need 84dl ripping chain in 3/8 .050 and you're set to go. Can get both from a ton of different places. There's off brand ripping chain available from Archer and Forester around $26.95 for a loop up to Oregon 72RD084G chain for $50-ish a loop (though Amazon has it for $39).
That UK site I mentioned has become the dominant milling supply place to all of the UK and Europe because they went to the effort of being milling specific, creating their own in house brand of mills and chain and some bars (Panther brand), carrying Stihl and all the other ripping chain brands, partnering with GB which makes outstanding bars to supply the entire line of GB bars from lo pro to .404, and supplying the rare lo pro drive sprockets for 60+cc saws which can't be found in the US except by special order from an obscure timber products company in Washington state. Most importantly, they matched everything up in ready to go packages. A few online shops are doing milling packages in the US now, but mostly for big bar milling setups. So it's still unnecessarily confusing to figure out the best milling setup for something like a Logosol in the US. And lo pro simply isn't available - GB (Aussie company) is the only company in the world to bother making lo pro bars over 20" aside from the high priced Cannon Super Mini ones.