These guns are cheap, people want to shoot and reload for them so, while I don't care much for it myself, I have tried out a few loads.
First, don't mess with .32 H&R or 32/20 unless you have a cylinder chambered for those cartridges. The .32 S&W or H&R is so undersize at the base as to be dangerous. The 32/20 is a better fit except the rim is much larger and thicker, my own Nagant won't revolve with 32/20 brass. And it is still too short. Revolver smiths agree that for accuracy the chamber throat and forcing cone are the most critical elements. Nagant chamber throats are cut to accept the full length Nagant case, making them grossly oversize for a .312" bullet and the Nagant has no forcing cone at all, being as the breech end of the barrel is also cut to accept the Nagant case mouth. Such jerry rig ammo may have been necessary at one time but today the proper Nagant ammo is available with boxer primers for reloading.
I first obtained and fired three varieties of factory loaded ammo, Fiocchi, PRVI and Russian match ammo. The Russian is Berdan primed and not easily reloadable but the Fiocchi and PRVI are normal Boxer primed.
Then came a search for reloading dies. I got a set from LEE but only the sizer is actually made for 7.62x38 Nagant, the expander, seater and shell holder are 32/20. The dies work sort of OK but the shell holder not at all. I got one from RCBS. It is a special order shell holder and cost over 20 bucks but it seems to be the only option.
These were the results of my shooting at 25 yards, all shots were a full cylinder and were chronographed as follows. My revolver would consistently throw 2 shots of 7 out of the group so I'm reporting the total group size / and the best 5 of 7 after the slash mark.
Russian match factory load---586 fps and 2.6"/1.5"
Fiocchi 98 grain FMJ factory load --672 fps and3.7"/2.1"
PRVI 98 grain FMJ factory load--641 fps adn 4.1"/2.8"
90 gr. Hornady SWC over 5.4 gr. AA-5--1043 fps and 5.4"/2.5" NOT RECOMENDED
90 gr. Hornady HBWC over 3.5 grains Trail Boss--954fps and 3.5"/2.6"
90 gr. Hornady HBWC over 3.2 gr. HP-38--858fps and 3.3"/2.3"
The Russian ammo wins the accuracy title but is Berdan primed and not easy to find these days. The AA-5 load is HOT and not recomended, I'd advise backing that down at least half a grain. Best results overall were with the 90 grain HBWC and about a toss up between Trail Boss and HP-38.
Bear in mind that this was just one group for each load and from just one gun, your results may vary, a lot.