Welcome. I have a .380 EZ and I use:
For range use, full metal jacket (fmj) with bullets weighing 90-100 grains. 95grn fmj is probably the most common loading manufactured. It has been in very short supply during this ammo crisis. Brass cased instead of steel cases cost a bit more, but most feel it works better in most guns.
Cost has been up to a dollar per round if you could find it, or $50 for a box of 50 rounds. That is more than double the normal price. If you can find a few boxes locally for $0.45/rnd you will be doing well. I see online bulk orders at about this price. I expect in 6 months it will be much more available and cost <40 cents per round.
There is a lot of 380 ammo imported from European manufacturers. It’s good stuff. The name brand American loadings are as good but some times cost more.
Do some searches here on the 380 EZ for good hints and tips. I love mine and have had no problems with it.