Use cash. Don't buy anything for this part-time business on credit.
Buy a good quality trailer. A 6x10 will be plenty big. A good trailer is something you can keep for life, whether you mow part time or not.
As you replace equipment, replace it with good quaility commercial grade equipment. Our first mower was a home-owner John Deere zero turn. We got 500 hours out of it and that was about all we would see. We would run home-owner 21" mowers and would get about a year out of them. Now everything on our trailer is commercial, and I can tell you it is well worth the money.