You don't want zig-zag stitches on vertical seams really no matter what (they'll pucker when pulled apart) so just use a straight stitch (if you did have lengthwise stretch and wanted to preserve it you'd want to ideally use an overlock stitch - but that's not a factor here) - and since you don't care about stretch you can just use whatever hem stitch you think would be most attractive/easiest for you (your call).
Personally, I'd just start sewing it and see what happens. Why worry about need for a stabliser if everything goes just fine ? I've never needed anything for any velvet I've ever used - including stretch ones, but some people do. Just try it and see what happens. If you have trouble controlling the fabric, then think about finding a solution to that problem if it does actually exist as a problem - don't make problems to solve before they even exist.
Being able to press the seams well will depend on the fibre content more than anything - the velvet isn't really an issue, just make sure you don't crush the front and it's just like usual.