Directory ( Searchable)?

Ive been racking my brain trying to work out the most efficient and easiest way to have a searchable directory as part of a wp website I’m building. The site is based around fresh produce – Basically people should be able to go on to website and search for a) a variety of vegetable b) a specific type of vegetable c) a particular grower d) Location of growers e) Month of availability of produce.
Is there a plugin that could do this or is there a way through catagories? Any solution would be greatly appreciated.