As I see it, you've got three main kinds of software you could look at.

CAD, GIS, and Graphics software.

CAD has been addressed, and Gameprinter has pointed out one Graphics tool you could use. Inkscape is another one, and has the advantage of being free and multiplatform.

GIS tools are what are used for real world maps and managing geographic information. Roughly speaking, CAD tools are focused on things that are self contained, while GIS tools are concerned with things that have a specific location on the surface of the Earth. (Obviously there's a bit of blurring together in the middle.) Free GIS software is available (I work for a company that supports and develops Open Source GIS Software). QuantumGIS is the big name in FOSS Desktop GIS. Adding the geospatial component does add complexity, but on the other hand, Web based GIS is well established so if you want to make this thing web accessible as you've described, then GIS has an edge there. Handling changes over time is also something GIS toolsets often support.

If you got professionals to survey your existing garden and want to use GIS, then you'd probably want to get the results in the form of "shapefiles" which are the de facto standard for vector GIS data. You can also often get GIS data (Vector shapefiles, raster DEMs and orthophotos, etc) from various levels of government, though it varies from place to place what's available.

Practically speaking, a vector graphics editor is probably more than enough, and GIS or CAD is overkill. But sometimes overkill is fun.