The answer to "should I include this redundant thing, just in case?" is always "no", unless there is a clearly defined reason why both are necessary (in which case they're probably not really redundant).
Every element you put on screen increases the user's cognitive load. Redundant navigation means the user may not immediately recognize that it is, in fact, redundant -- if you were to include both the hamburger and the navbar, the user would have to examine both of them in order to determine that they are in fact the same thing.
So that's the easy part done. The harder question is, given that you have to make a choice about how to display the navigation, which is the best choice?
In all cases, you should devote screen real estate to whatever is expected to be most useful to your users at any given time. The times at which the user is most likely to need access to navigation are
- when they first arrive at the site, and don't yet know what content is available
- when they have finished reading a page of content, and are ready to find something else to read.
The time at which the user is least likely to need navigation is
- when they are in the middle of the page, halfway through reading a piece of content.
Therefore: place navigation at the top of the page, because that's where users expect to see it, and that's where they are when they first arrive at the site.
You can also place navigation at the end of the page, because that's where they are when they finish reading a page of content -- but this is often unnecessary because users are accustomed to scrolling back to page top to find the navigation, because that's where it always is; and because all major mobile browsers support single-tap scroll to the top of the page (because that's where the navigation always is). Footer navigation is generally best for links to related-to-this-page links (which wouldn't fit well in the main navigation) or for boilerplate or incidental items such as credits, legalese, site maps, etc (which ditto.)
In your particular case, you only have three navigation categories, which can be listed at the top of the page (which has the visibility advantage over tucking them away inside a menu.) The only other elements inside the hamburger are your "login" and "register" links (which are also redundant with each other: you only need one of them, which leads to a combined login / create account page.) This, too, could easily be represented inline at the top of the page, rather than tucked into a menu.
Therefore: use a top-of-page navbar with a "log in" link above it. Don't use the hamburger at all, as it serves no real purpose (floating it is counterproductive, as described above; static at top of page is just redundant.) Bring it back only if you add more content categories such that inline navigation would no longer fit comfortably (and use it instead of, not in addition to, inline navigation.) Don't make anything floating or sticky; trust that the user knows how to find the top of the screen if and when they need it.
TL;DR:
In general, which is more important? Your content, or your navigation?
If it's the content, then the screen real estate should prioritize the content. Don't clutter the viewport with sticky navbars or fixed tabs, especially on mobile devices where screen real estate is so limited, because all that accomplishes is getting in the way of what the user is trying to do.
If it's the navigation, write better content. :)
