Groundwater fluctuation is permanently occurred during the year. GW variation sometime exceeds 1m. high water table level occurred in spring and vise versa in winter. Briefly, mapping process is easy and needs few measurements for water table level in an area to construct a contour map
1. Database to handle groundwater mapping data: Several open source and paid ones are available. I will recommend Postgres (open source). Its free, flexible and can accommodate high data storage and throughput (if correctly configured).
2. Groundwater mapping/modeling application. I'm aware of only commercial ones. The choice of which to use will depend on your needs and licensing costs.