For printing, just go to a FedEx Kinkos and use their color laser printers; I usually used 24lb paper I believe. Any print service place (Staples does it too I believe) with color laser printers ought to do the job.
I personally can't imagine leaving out covers to issues, but it comes down to personal preference, like most things with binding. If don't care about them, you don't have to include them obviously.
As far as thicker covers, if they're cardstock (like prestige format books) I strongly recommend scanning and reprinting them. For something like Batman #500, and if it's only the one cover, it might be okay, but the book will probably open to that page rather than lay flat (this goes doubly for prestige format cardstock covers, that's why I recommend scanning and reprinting them, even if it's only one) I can't quite recall it's thickness though - if it's too thick, or you are worried it is, you could always print the standard cover: https://cdn.shopify.com/s/files/1/22...g?v=1502056157
I found that decent-res version.