For the money your looking to spend your not going to get much in the way of any type of ride on mower and anything on craigslist ( Stander, ZTR ) in the 1500 range will most likely have a lot of hours. Using a push mower to do a quarter acre your not going to make a lot of money either when you consider the time involved to mow between 7000 - 11000 feet. Your best bet for a ride on if you want new would be a Cub Cadet LTX 1040 Lawn Tractor you can get that for around $1300 and even then you'd be looking to expand your budget to purchase a trailer, push mower and handheld equipment etc.
Depending on whether your serious about the business or not should determine how much money you need to drop. There are other considerations to the business beside equipment like a license, Insurance, advertising just to name a few. If your going to do it right your not going to show a profit for probably two years, It will take you that long to get out from under your start up cost.