I usually do cotton on both sides (though I have done ones with a flannel back). Keep in mind that the cotton will get softer & softer with each wash so I usually wash mine a time or two before its first use. imho, flannel is used for aesthetic/tactile reasons. I like to do a lot of applique & it's much easier to applique on to cotton so that's what I use. The one tip I'd share regardless of whether you use flannel or quilter's cotton, is to make sure the fabric is a good thickness (esp. if you're buying fabric at a box store like Joann, Hancock's or Hobby Lobby). If it is too thin, it will not wash as well & will tear easier). Other than that, pick what you love.
I've yet to get any complaints from the babies.
Congrats on your little one! How exciting!