First thing I would do is slug my bore before I went any further on bullet selection. Second although the AKM and the SKS both shoot the case cartridge and use similar gas operated system that where the similarities end.
The AK was designed to be a machine gun first and foremost,it has a lot of design features that make it a great weapon but will put limitations on it's accuracy at longer ranges. The SKS is much closer to a rifle and seem to respond more favorably to handloading but the AK can be made to shoot more accurately by feeding it consistent ammo. Since your using your AK at close range that's probably a moot point but you might not always have that luxury and every little bit of accuracy you can gain might make the difference.
As far as component bullets I've tried I get great results with any of the Hornady .310 offerings FMJ,SP and V-MAX,in .311 I use either the Prvi Partizan 150 gr. BTSP or the Speer 150 gr. flat base Hot Core SP. I like the Prvi bullet because it has a large exposed lead tip that expands well at X39 velocities at short range.
On powder my two favorites are AA1680 and Reloader #7,I like Reloader #7 because it works with all bullet weight I tried for 123 up to 185 gr. as well as cast bullet loads. H335 is a good powder but I don't like it in the X39 it not as efficient per grain,requires 4+ more grains to achieve the same MV as the two powder I mentioned and you have to compress the load to get top matching MV.
Another thing to think about is MV vs. bullet expansion in the X39. In a 20" barrel your going to get about 2100+ fps. MV with the heavier constructed bullets at that MV bullet expansion may be an issue if you only hit soft tissue rather than some bone and will do very little damage to the vitals. I would prefer a shoulder or head shot if I hadn't tested the expansion characteristics of my chosen bullet in my rifle. The Barnes bullet would probably be the exception to the rule.
Wolf 154 gr. SP taken for a 180 lb. deer penetrated the chest and lodged in the rear hindquarter.
For primers in my SKS both of which have free floating firing pins I use either the CCI#34 Mil-Spec primer which is rated as a Magnum primer or the Wolf LR and LRM primer,both the Wolf primers are suitable for Mil-Spec type weapons and have harder primer cups. I can use Win LR primer in my Chinese safely,it doesn't put much of any dimple on the primer but I use them as a last resort since I have plenty of the others.
Also none of the reloading manuals data list the use of a magnum primer in the X39 case so work your loads up from the starting load if you use these primers. Make sure regardless of the primer you use that there seated flush preferably a few thousands below flush. you can check that by setting the primed case on a hard flat surface and tip it to one side and watch to see if it wobbles or goes straight upright,you can also use the back depth gage on your calipers to check the primer depth.