Some very interestinh info on here! Even a little fight...
As for equipment, maybe you could get something like a 36"walk behind used on craiglist. The Toro Proline 36" is very popular and does a good job. I don't think you will be able to get anything fancy for 1500$, but it will get you started. Spend the less possible on useless stuff. Concentrate on buying equipment that will get your jobs done faster. The faster you go, the more clients you can get = $$$. Get yourself a budget also. Many people in America donnot have a budget. Even for there familly and that can cause many problems. Now, with a budget, you can control the inflow and outflow of your cash.
As for charging, it is your prices! Dont just phone other companies and ask them their prices and lower yours! You can surely phone to make sure your prices are not way out tho. To defend your price, you must stand out giving outstanding service with good equipment. You want to be looking on the job and show your clients you do this with pride and professionalism. Get some t-shorts also with your campany name!
Dont let the other companies discourage you! Also, get an accounting system to enter all expenses, and invoices. This can give you an idea on your profit margin.
Once you get real busy, maybe you could think about a helping pair of hands! It goes much faster and you are less exhausted at the end of the day.