Should be "Serious gardeners like my wife and I always use organic fertilizer."

The reason is that "I" is subjective, not objective. It looks like "serious gardeners like my wife and I" could be seen as the subject. If not, "Serious gardeners" is and "like my wife and I" is descriptive of "serious gardeners." In any case, "my wife and I" needs to be subjective like "serious gardeners." Therefore me and myself are incorrect. One could simplify the sentence to say, "Serious gardeners always use organic fertilizer." One could say "My wife and I always use organic fertilizer." "My wife and I" is subjective just as is "serious gardeners." One wouldn't say, "us always use organic fertilizer," and that is a good way to check the proper use of pronouns like I, me, etc.
People often have a problem with getting the subject, object correct in a sentence with pronouns, because of music, media and other people. Even those who should know better use it incorrectly.
An example would be, "Me and her went to the mall." "Me and her" are objective not subjective. One could substitute "us" for "me and her" and one would get "Us went to the mall." This is obviously incorrect. So it should be "we went to the mall," and "I and she," but maybe better, "She and I went to the mall." Hope this helps. Substitution of pronouns can be a good method to check if in doubt, as well as looking at what is subject and object.