If you aren't familiar with them, a good source of tools and supplies for mini lathes is Little Machine Shop.
My first lathe was a 6" Atlas and since I was just
getting started I wanted some off the shelf tools that would work for me without having to learn how to grind
tools. LMS sells kits from A R Warner which have both HSS and carbide inserts. I got started with the
HSS inserts and had good results with them. They have their limitations, but I've made a lot of parts
with them, they're dead simple to sharpen (I hone them on a flat stone) and though folks complain about
the cost of inserts, the kits come with spares and I've never had to replace one.
The premier source of tooling, parts, and accessories for bench top machinists.
littlemachineshop.com
Here's another option: The Diamond Tool Holder
This product is made in Australia but available in the US through Village Press:
This is an example of a Tangential tool, which is an old concept and not invented by Diamond.
The tool holds a standard piece of HSS steel (cheap and available) in an almost vertical orientation
which, when ground at an angle produces a diamond shaped surface: the point of contact with
the work is one corner of the tool. It is sharpened in a jig supplied with the tool on a bench grinder
or belt sander, and is very quick and easy to accomplish. Mine has become my go-to general purpose
turning and facing tool (it does both without changing your setup) and I use it all the time.
Lots of YouTube vids available for this tool. They come in different sizes, so it's necessary to choose
the correct size for your machine. Diamond's website explains this.
Having said all this, it's still a good idea to learn to grind your own tools.