If you can successfully outsource a non-core function, then do so. HR is one of those things that can be successfully outsourced particularly at the small scale.
The only maybe gotcha with outsourcing the HR function is that, while you can outsource the routine tasks (issuing payslips), you can not outsource to an outside firm the legal obligations surrounding employee contracts, employment law, obligations to pay correct payroll taxes, etc.
If you go the route of outsourcing HR, you may wish to consider investing a bit in HR consulting with the aim of educating yourself about employment law in your legal jurisdiction.
The only maybe gotcha with outsourcing the HR function is that, while you can outsource the routine tasks (issuing payslips), you can not outsource to an outside firm the legal obligations surrounding employee contracts, employment law, obligations to pay correct payroll taxes, etc.
If you go the route of outsourcing HR, you may wish to consider investing a bit in HR consulting with the aim of educating yourself about employment law in your legal jurisdiction.