When you reproject your raster there will be a resampling, so the new data will be degraded. It is therefore better to convert directly from a feature class with the output CRS that is most suited to your need, in other words you should reproject your feature class that is currently in WGS 84 into a projected CRS if you want your final data to be in WGS 84. The conversion of feature class will be exactly reversible if you don't change the datum, you just need to be aware that only the vertices are projected. therefore, if you have long segments without vertices, it is recommended to "[densify]" before your project.
The size of your pixels will affect the precision of your feature to raster conversion, as well as the precision of the resampling. It will not, however, affect the accuracy of the area of your polygon linked with projection (if your projection is not equal-area, the average over or under-estimation of the polygons area will not depend on the pixel size)
Now let us consider the choice of a CRS.
With a geographic (lat/long) coordinate system, the cell size will be expressed in degree. The cells of a raster of the same width and height everywhere, so the actual (on the ground) extent of grid cells will change depending on your latitude. If you want to know the size in meter of on cell in a lat/long system, you can have a good approximation with the knowledge that one degree is approximately 111.3 km at the equator, but that the width of your pixel has to be corrected by the cosinus of the latitude. Therefore, if you need a final raster in Lat/long, forget about an exact cell size in meter and use a convenient approximation based on your location (e.g. the minimum or the average of a degree of Lat and a degree of Long). For instance, at a latitude of 60°N, a square of one by one meter is approximately 8.9847e-6 degree in the Y direction and 1.797e-5 degree in the X direction.
With a projected coordinate system, the cell size is expressed in a cartesian system (with a unit in meter, in feet...) and this value is constant everywhere on the grid. Of course, you are in a projected coordinate system, so there is a small distortion due to the move from a sphere to a plane, but you should not be too much afraid of this distortion because you can usually find local projection that reduce the distortion below the error range of your measuring tool/method. Therefore, if you don't need to have a raster in Lat/long, use a (local) projected coordinate system where you project your feature class, then convert the pojected feature class to raster.
Remark : If you do not perform your analysis in spherical geometry, I recommend working in a projected CRS.