The basic goat's cheese you get at the store ("chèvre") is a basic soft semi lactic cheese. It is consumed fresh so it is less stable ( = spoils faster). This simple goats cheese is not aged thus never gets the chance to build a rind and take on the characteristics of its counterpart; the Crottin.
The process for making Crottin actually starts out just like making that basic goats cheese, so these two are very much related. In fact, during the first 2-5 days of Crottin's life it would taste and feel just like a good goats cheese. Crottin however has inoculated bacteria in it which develops rind within a few short days. This stabilizes the cheese, kills off competing spoilage bacteria and enables it to age and assume far deeper flavor/texture characteristics. (In theory, spraying store-bought goats cheese with this bacteria and aging it - will produce a Crottin within a couple of weeks).
The best thing for you to do is to taste Crottin and feel its flavor, aroma and texture. This way you can to gauge your target for making such cheese. Crottin is a casual country table cheese; not a fancy expensive cheese. It should be easy to find at a cheese shop or places like Whole Foods. WATCH OUT though; Some American brands sell simple goats cheese under the name "Crottin" to confuse consumers without actually doing the hard work to produce it... Do not be fooled! Get the genuine French version (Crottin de Chavingol or Crottin de Campcol). It is rustic in appearance, much drier and flakier, more citrucy and nutty, with a pronounced feeling of barnyard and grass.
Genuine French Crottin de Chavingol
Hay - I use French hay that is meant for cheese shops and cheese aging facilities. I get mine from a cheese affineur here in New York but you can ask your local cheese monger if they want to sell you these mats. They are inexpensive. You can also just use loose hay if you have it. This isn't a fussy cheese.
Here is a photo I took in an aging cave facility where you can clearly see the Crottins aging on mats of hay: