How deep are your pockets? You can spend a few grand on lathe tooling without breaking a sweat.
I would recommend you buy some HSS blanks and learn to grind some basic tools. High speed steel is way better for low horsepower machines.
If you really want inserted carbide, you'll want to brush up on the insert geometry nomenclature. There are a lot of letters and codes to keep straight. Size, style, shape, grade, coatings, all kinds of factors. There's so many its very hard to keep it all straight.
For you to start, I would reinforce matt_i's recommendation and get something positive rake. You'll be chasing your tail with a negative rake insert. Negative tools NEED horsepower and rigidity to run. If you don't understand what the difference is, you'll want to brush up on how cutters are ground and why. See HSS recommendation above.
As far as retailers go, MSC has the most, but they are generally very expensive. I don't buy from them unless I have a really good coupon or sale.
McMaster-Carr has lathe tooling, you just need to know what you want.
Travers tool is another good source, as well as KBC tool.
Brands are a fussy thing, you can have good results with most of the big boys. I run mostly Iscar and Tungaloy inserts. I have them in Hertel, Iscar and Kennametal holders. I have some Seco insers in my mill that I like too.