As others have emtnioed, the low cost Hornet bullets work fine.I am sort of partial to the Remington plated HP 45g slugs when handloade for low cost Hornet reloads.In a "no holds barred" load, I like Hornady V max or Sierra Blitz King 40g plastic tipped slugs..
If you are going to handload, I do have two basic tips based on about 25 years of fiddleing with Hornets.
1) Only size about 2/3 of the way down the neck.In most Hornets this leaves sort of a second shoulder along the neck ahead of the real shoulder.Why? ebcuase the unsized rearward postion of the neck as firefromed really helps center the round in the chamber.There is plenty of neck in the front 2/3 to hold the bullet when resized.Using this technique, I have gotten groups smaller than 1/4" at 100 yards with factory chambered Hornets with good bullets and a variety of powders..
2) Use Hogdon LILGUN powder.Besides producing accurate loads and good velocity, this powder's MAIN advantage as I see it is it produces velocity equal to top end WW296,H110,IMR 4227 and other long recommended Hornet powders at about 70% of the pressure!! Most LILGUN loads run less than 32,000 CUPS while other powders run about 40,000 ++.This fact ,along with the neck sizing mentioned leads to GREATLY extended case life with the thin Hornet cases.
I do not have a Handi in the Hornet yet, But I soon will and you can bet I will be applying the above techniques where ever I can when reloading for them..