Independent Baptist, very strongly pre-Trib, very missions minded, I tend to think that goes hand in hand with it but it could just be because my church is; but it does make sense that one feels a need to win souls because one knows time here could be very short.
I grew up Lutheran, went from head knowledge to heart knowledge reading the Bible in college, and listened to services on the radio or TV for a few years before I started going regularly to my church after law school - so I really don't rememberever hearing any different except for Pat Rogbertson's show, which I took with a grain of salt anyway because of other things; the Lord knew I wouldn't be within walking distance of a good church consistently for a few years and gave me a strong sense of discernment when I was first saved. (Of coruse, claiming the promise of James 1:5 about numerous areas right away helped, too; I prayed and believed God would give me wisdom about things and He did.)
I don't recall when the first message clearly on the Rapture was that I heard, but it was surely within the first 2-3 years that I attended my church on a consistent basis. And that was with one pastor leaving after a year and then visiting pastors for quite a while; the Lord had the right man he was preparing, though, and when he came in 1999 it was definitely a wonderful thing, as he has done a great job of teachinga nd preaching the rapture and all the rest of the Bible.
John 3:16 (KJV) For God so loved the world, that He gave His only begotten Son, that whosoever believeth in Him shall not perish, but have everlasting life.