I had a meet the baby party - that my sister hosted. Awesome and I'll definitely do it for every baby. But I was really serious about it being a "Meet the Baby" party, not a "Give me a gift" party. So I had it pretty soon after his birth, so that people could meet him -- it seemed dumb (to me) to have it a couple of months after he was born...by the time the party happened, most people would've already met him!
To keep it casual, we did facebook and email invites for most people. It was literally a "come anytime between 12:00 and 3:00 to meet him, grab a hot dog, nachos or cracker jacks and meet our son" (we did a baseball theme). For grandparents and such that might want something a little more formal, I did make an invitation, got it cheaply printed on a postcard but with no dates or time. Then when he was born, I used a Sharpie to write in the date and time.
I did (which many would disagree with) write on there "Please no gifts"...which in most cases kind of implies that they should bring gifts. But, for me, this was the first of this kind of party in the family and I really wanted to make sure that it was clear that this was very casual, please no gifts, come only if you can kind of event.
ETA: I didn't get many gifts at all. I did get some cards, but not major gifts. And we probably had 60 people or so file in and out of there. I was a FTM who didn't even have a shower, so the few gifts that I did get were from aunts who would've gotten me a gift anyway. I did get a couple of children books, but really, most people didn't get us anything and if they did, it was a card. Which was exactly what I wanted.