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).
Of course, you take all the cool stuff from CSS3 and the new JavaScript that people call HTML 5 and isn't, and remove it from "HTML 5" -- there is little if anything of value or improvement. The people trying to promote that bloated, redundant halfwit garbage slap all the cool stuff that has NOTHING to do with a markup specification under the "HTML 5" banner because without it... Well, the Emperor is standing there bare for the world to see.
The only things from 5 I'd suggest spending any time on is AUDIO, VIDEO, CANVAS and MANIFEST. The first two are redundant to HTML 4's OBJECT element and are basically shoved down our throats thanks to Apple's sour grapes over losing the media formats war over a decade ago and freetards raging against the machine. Manifest is actually useful if you want to build web applications... and CANVAS is more a javascript thing, only works when JS is enabled -- which is why it has NO BUSINESS even having a tag in the specification in the first place. 
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.
