You can actually start using schema.org based Breadcrumb markup now. Google is supporting it and it's good. You can choose your format JSON-LD (preferable), RDFa, microdata. And another good thing is that you can define multiple breadcrumbs if your products need it, which will usually be the case.
With Microdata support, you can do this:
<ol itemscope itemtype="http://schema.org/BreadcrumbList">
<li itemprop="itemListElement" itemscope itemtype="http://schema.org/ListItem">
<a itemprop="item" href="https://www.yoursite.com">
<span itemprop="name">Home</span></a>
<meta itemprop="position" content="1" />
</li>
›
<li itemprop="itemListElement" itemscope itemtype="http://schema.org/ListItem">
<a itemprop="item" href="https://www.yoursie.com/category/books.html">
<span itemprop="name">Books</span></a>
<meta itemprop="position" content="2" />
</li>
›
<li itemprop="itemListElement" itemscope itemtype="http://schema.org/ListItem">
<a itemprop="item" href="https://www.yoursie.com/category/books-literature.html">
<span itemprop="name">Literature & Fiction</span></a>
<meta itemprop="position" content="3" />
</li>
›
<li itemprop="itemListElement" itemscope itemtype="http://schema.org/ListItem">
<a itemprop="item" href="https://www.yoursie.com/category/books-classics.html">
<span itemprop="name">Classics</span></a>
<meta itemprop="position" content="4" />
</li>
</ol>
Note the usage of position values and it's advised to use ordered list ('ol').
After you do this, you can ask google to show your site name instead of the 'Home' that's at position #1. For achieving that, use this on your homepage:
<head itemscope itemtype="http://schema.org/WebSite">
<title itemprop='name'>Your Site Name</title>
<link rel="canonical" href="http://www.yoursite.com" itemprop="url">
For anything, refer here: https://developers.google.com/structured-data