Q: On my deed it says that only one (1) single family residential home with a garage can be erected on the premises. Does this mean I can't put up a shed or greenhouse?
A: Yes, if the deed specifically limits the erection of any structures except for one single family residence, and one garage, then you are indeed restricted from erecting a shed or greenhouse. However, what you wrote is a little ambiguous. It could be construed as meaning that you can only erect one house and one garage (i.e., not two houses or two garages). If you can quote the deed exactly as it is written, then I will have a better understanding.
Q: Does this also mean I can't have a home based business?
A: No, that shouldn't prevent you from having a home business, though your HOA (if you have one) may prohibit it, and your local zoning may be for residential use only. But it ultimately depends on what kind of business you're talking about. For example, I answer these types of legal questions online from my home. There is no problem. But if I had clients come to my house for consultations and meetings, then that would likely be a problem.
Does that answer your question? Please let me know if you need clarification, as I am happy to continue helping you until you are satisfied.