Don't these cache programs only work on repeat visitors since it has to be viewed by the user one time before it can be cached? How is this beneficial to me if I'm only sending a user to this sales page once?
Yes, a page is cached only after it is viewed for the first time. If you're creating a unique landing url, per visitor, a cache won't help you.
Also, I heard something about how you have to manually cache the site every time you change something on your blog, like making a new post. Is that right?
Most of them will purge cached pages if you update them. None of them, as far as I know, "prime the cache" in the way that you're asking. The typical use case is lots of visitors to the same url. So, the first visitor gets a slow load, everyone after (until the cache expiration) gets a fast load.
How much work is involved with these plugins?
Not much after you configure them (cache expiration time, urls to exclude from caching, etc.)
If you are are indeed using unique urls, per visitor, then you need something other than a page cache. The biggest bang for the buck would be an opcode cache, like apc, or the one that comes by default in php 5.5+.
Also, mentioned earlier, a lazy image loader that loads images just before the user scrolls down to them.
And, using a theme that isn't heavyweight. Most wordpress performance issues are caused by third party themes or plugins. A vanilla install, with the default theme + an opcode cache, is reasonably fast.
