I just looked at some of the most popular websites, and few have a Home link. Even Bright Journey and Stack Exchange do not. It seems like the logo is a more popular choice as of late.
To be fair, I think it depends on how your logo is arranged with the rest of your navigation. Look at the top navigation here on Bright Journey. The "logo" (just text) is embedded within the nav. If the two are separated by much, you might consider dropping a home link in instead.
A couple of related thoughts:
1. This is insanely easy to split test. When/if you have enough visitors, try it with and without the Home link and see what the traffic patterns tell you. Just because most major sites do one thing doesn't mean it's necessarily a good fit for your users.
2. You probably have bigger fish to fry than this. Most startups do. Don't spend too much time thinking about it. Pick the one that you think makes the most sense, maybe do a quick round of split testing (or not) and move on to the bigger problems.
I think it depends on what sort of website you have. If you have a web app like Bright Journey, then no I don't think it is required. As your home page is simple a landing page welcoming you into the app. However if your site is an information website or a directory of some sort, then yes I would have a dedicate home button. As a rule of thumb, I always leave the home button there, as well as link up the logo. If it looks tidy enough, and there is some reason why visitors might need to get back to your home page then why not