Reproject, then clip or clip, then reproject?

I have a fairly simple question. I have a global categorical land cover map that has no projected coordinate system (i.e. it uses the EPSG:4326 coordinate reference system with no projection). My study region encompasses an international regional geographical scope (for e.g. South Asia). I have to apply a projection to the data because I need the units of measurement to be in metres and not degrees.

My question is this; do I

1. apply a projection to the global map, then clip it to my region of interest (using a similarly re-projected vector country boundary layer)…or do I

2. clip it to my region of interest using an un-projected vector country boundary layer (i.e. EPSG:4326) and then reproject the resultant clipped raster to a suitable projection?

I am unsure which method is the proper method, can someone enlighten me? Or maybe they make no difference at all. But just thinking about it, it sounds like the first option is more sound (robust) as opposed to the second, primarily because my input data is a global dataset. Additionally, one reason I am thinking so is because I find it difficult to get appropriate projection systems that cover a regional landscape, but it is relatively easier to find multiple global projections.