Hey
@mikepcservice!
Backlinking is an art form. I like to call it earning links, because links that are earned via great content or great reputation are the ones that have the most value. It used to be thought that links with a high DA carried more weight, but it's not really true anymore. What you want (for the most part) is links from sites who are (1) an authority in their field, and (2) related to the content on your site in some way.
For a local business, I like to see links from the local news papers doing an op ed on the business, or from other business owners recommending the business. I also like to see links form local chambers of commerce. These sites may not be huge, but they show that the business is one to be trusted.
The reason great content trumps links is that it's the content that earns the links, if that makes sense. If you wrote an amazing blog post about something that was used as a reference source (and linked to) within someone else's content on a similar topic, THAT's a good link...and those are the links Google is looking for. It has nothing to do with DA, though looking at DA is good to make sure the site linking to you is not a spam site or a link farm. Moz has a tool that's pretty good for this, and it's free to a certain point.
As for tools, I use SEMRush a lot, and I've used Moz Pro in the past. It's nice to be able to see some of the links that competitors have, their trust scores, and maybe find some sites my client can try to earn links on (such as the local chamber, schools or charities that give links to local sponsors, local news media, etc... Notice these are all links that would come naturally if the business is an active participant in their community.) But mostly I use it for new sites I'm taking on where I want to know if they have any unnatural links that may be red flags - especially for older sites. I have no idea what black hat shenanigans may have gone on in the past.
Keep in mind that no tool will show all links. Search Console will show some link data, and it's free. Majestic is considered to be the most comprehensive, and many tools such as RavenTools pull from Majestic's data.
I hope this helps!
Cherie