Rob, 'MDF' is Medium Density Fibreboard, available in sheets of various thickness from virtually ant hardware/timber store. It's what's normally used in the production of 'flat-pack' furniture, although with a veneered finish for the latter, and is a finer version of the coarser 'chipboard'.
It's fairly inexpensive, relatively light, and easy to cut to size, with a thickness of around 10 mm or 15 mm (both 'standard' gauges) being ideal for base-boards.
Grass can be simulated with model railroad 'scatter' materials, supplied in bags, or the 'hairy mat' grass matts, in rolls, both available in various 'season' shades. The choice depends on the scale required. The grass mats, which have individual 'blades' of grass (as seen in the pics I posted) can simulate longer grass in smaller scales, or shorter grass in larger scale, whilst the 'scatter' materials are basically dyed sawdust, although very fine.
Both can be attached to the base with the use of PVA (white glue), and an advantage of the matts is that the 'grass' can be removed by wetting the required area, allowing the paper backing material to be painted to represent earth, mud, sand or whatever, as desired. Again, examples of this are shown in the pics I posted.