That beautiful 624 with a 4" bbl. is my #1 grail gun, Shoe....glad you've got it....as to loads, I've used Skeeter Skelton's famous prescription: any good LSWC backed by 7.5 gr of Unique for 900-950 fps in 44 special brass of course.
I own four .44 Spl's: a M-24 6.5", and three Ruger Flat Top BH's (two 4-5/8" and one 5-1/2"). And all of them thrive on that old Skelton load. It's a reloader's cartridge load though. You can also duplicate Skelton's favorite with: 6.7 gr of Win 231, or 8.0 of Herco as well. Bullets are easy to find. Missouri Bullet Co's 240 gr LSWC does nicely but try to order the softer one, BN 12 IIRC.
As a combat load, the above combination is super accurate, with plenty of smack for most any purpose and still allow you manageable recoil. Here on our farm and my son's next door, we've used it to finish off several wounded deer and two horses. Penetration it's got!
Recommendation: Get into reloading...you probably won't save a nickel though primarily because reloading will allow you to shoot more for the same amt. of money. Too, you'll find it allows you to tailor your loads to a particular gun, getting better accuracy and one that better fits your needs.
HTH's Rod
Here's one of mine...with some stocks I made up for it. Hazy in the background is my home range with some railroad tie plates used for plinking off the deck. The cross fence is 25 yds & the distant berm is 93 yds from the porch rail.