To answer your question about Internet Explorer, it will warn users about any site whose certificate is not signed by an IE-known (unfortunately called "trusted") CA. This includes for your own CA and for self-signed certificates. It will also make a warning if the domain in the certificate is not the one being accessed.
If this is a private site, you may not care so long as you are getting link-level encryption (and are you that fearful of someone sniffing your traffic?). If there is public access and you want SSL, then get a signed certificate from a recognized CA, as others have already advised.
