Small business grants can be helpful to jumpstart a business but getting one is no cakewalk. Your best bet will be to focus on local grants (city and state) as the competition is less severe than at the federal level and the eligibility requirements are not as strict.
It is also important to understand that most grants are given to non-profit organizations for programs and services that benefit the community or specific group of the general public. In addition, usually grants that are available for a startup for-profit business, focus on research and development in medicine, technology or energy.
There are exceptions to the rule but the likelihood of attaining a small business grant doesn't look that promising based on your business model. With that said, it is crucial to have a deep understanding of the local granting organization. Don't apply unless you qualify and have verbal confirmation from the coordinator at the granting organization.
If you have difficulty finding a grant that your business is eligible for as I expect, you should consider other funding options. The Small Business Administration (SBA) offers loans to startup businesses. You can also try to attain a bank loan.
Good luck with the paintball store and finding the capital you need to get started.