The simple answer is that yes non profits and charities do pay staff if they have the money to. However, how your organisation develops will have some bearing on what you can and cannot do.
A "non profit" tends to be an organisation declaring they are non profit, there are not the same sort of checks and balances like charities have to go through outside what you do for Companies House.
So, it sounds like you could start doing that straight away if you aren't already...
A charity is clearer, but it is time consuming and complicated registering to be a charity, a number of orgs are turned down and they have to re-apply which is very costly. But naturally there are both perception (in the eyes of the public, your beneficiaries & your donors) and tax/discounted services benefits to being a charity. Plus some funders will ONLY fund charities, this might also apply to local authorities/PCTs.
If you receive restricted income (ie must be spent on a particular project, so an eg for you "drama for those that were homeless"), through a grant/donor that may have a bearing on staffing allocations Although you should be able to manage this as you'll be applying for the funding!
You could opt for a Commuinty Interest Company, which is between the two. I believe there the regulator "check" that the salary of the lead person is reasonable. Have a look at this link - www.socialenterprise.org.uk/pages/frequently-asked-questions.html
I am guessing that being (and acting like) a non profit would be your first step, and a way to ensure that there are checks and balances is to establish a small Board/committee of external people in the same way as a charity has trustees - www.charity-commission.gov.uk/publications/cc3.aspx - so that it isn't just you and the money! Lots of non profits I know "act" like charities, even if they are not registered charities.
Good luck, sounds really good.
WS