I say learn HTML 4.01 STRICT FIRST, because HTML 5 is a "superset" of HTML 4, which means most everything you learn with the current recommendation (4.01 Strict) can be applied and used in HTML 5.
Though if you learn 4 STRICT first, and learn to use it properly, you'll quickly find that HTML 5 offers no real legitimate improvements, and in many ways is carefully crafted to undo fifteen years of progress... to the point it's a bit shocking anyone who actually knows what HTML is and how to use it would choose HTML 5 by choice.
Also, be leery when people talk about things like responsive layout, media queries, etc, in the same breath as HTML 5, as those are CSS3, not HTML 5, have nothing to do with writing markup, and are more an attempt to use HTML 5 as a sick buzzword than it is a legitimate use of the term. There is NO reason you can't do all those things with HTML 4.01 STRICT and/or XHTML 1.0 Strict. (which are basically the same thing with a couple minor syntax changes).
Basically, you want to learn to do it right, learn semantic HTML 4 Strict, and only look at HTML 5 if you need some of it's crap to support Apple users being told they don't actually own the computers they bought, or are going to dive into web applications. Learn about semantic markup -- aka using the tags for what they mean... and learn about separation of presentation from content.
... and the big mantra to keep in your mind -- if you choose your HTML tags based on their default appearance, you're using the wrong tags for all the wrong meanings. Just as if you are saying what something looks like in your HTML, you're doing it all wrong.