I want to learn how I can get a grant(s) to purchase equipment and then contract with the government once my business has started do business with the government?
The is no way to receive a business grant to purchase equipment. I recommend that you focus on having strong business credit which will allow you to purchase equipment for your business without personally guaranteeing any of the purchases.
There are few, if any, grants available to for-profit businesses unless they have developed a new product or technology that is in the national interest. If you want to contract with your city, county, and/or state to provide lawncare services you will first need to establish your business, then register with your city and state purchasing departments. Most agencies put contracts for landscaping out to bid annually, so you will need to watch the city/county/state web sites for bid opportunities. If you have local federal buildings that might need landscape maintenance, you would need to register with ccr.gov, the watch for bid opportunities.