This is the tool I mainly use for my own SEO projects, after trying quite a few. It is a paid tool, but the free version has almost the same features, with mainly the disadvantage that you cannot save your projects.
It is a suite of desktop tools with 4 extensions. The ones I use most are the Website Auditor (running SEO audits for my sites), Rank Tracker (to see how I do in Google for my saved keywords), and the Link Assistant, to track backlinks for my site.
Instead of paying monthly, you only pay a limited one-time fee, so this software is very cost-efficient. I have also written an extensive review of the software, feel free to check it out.
Especially for smaller websites, this is a very nice SEO tool to play around with. Mainly because it is free for sites with less than 500 URLs. A license is also available to check larger sites.
This is a paid tool, with a monthly fee, depending of the which features you need. But out of the many SEO tools that exist, this is probably the best there is.
You can always sign up for a free trial to test-drive the tools, see the link below:
This is a very useful little tool for everyday SEO purposes while browsing. It is a Chrome extension that you can easily launch for a page to check SEO parameters and domain information. But it can also audit the links on a page, especially for checking dead links. Best of all, it is free!