Please follow below mentioned SEO checklist for launching a new website:

Designate a Keyword for Each URL on the Site
Website Accessibility, UX, and Crawling
Set up the Tracking Systems and Important Services
Don't Forget Link Acquisition
Do those pages load fast from everywhere?
Schema, rich snippets, OpenGraph, etc.

Thanks

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SEO is divided into two parts: On Page SEO and Off Page SEO.
On Page SEO: On Page SEO is optimizing each and every page for better ranking on search engines.
Off page SEO: Off Page SEO is link building techniques that help you to rank better in search results pages.
Both SEO is important but On Page SEO is more important.
It is possible to rank higher in search engines without doing off page SEO if you have done On Page SEO perfectly.
At first, you have to focus on your site design, make it attractive but professional, easy nav bar, page loading time and more. If you are in WordPress then Web Host is really important. Select perfect web host such as Bluehost, A2 hosting, InMotion, Dreamhost, WPEngine and more.
When your write content, focus on the quality of your content. Write top quality unique content.
Keyword research is the most important On Page SEO technique. You do it before writing. You have to select low competitive keywords.
You can use KWFinder, SEMRush for finding the most profitable keywords.
Select eye-catching but attractive title, make your permalink short and sweet, just add your keywords on permalink, use heading tags, add keywords in all heading tags, internal&external linking, multimedia and more are on page SEO techniques.

Do blog commenting, guest posting, join forum sites & Q&A sites and take part in the different discussion.
All these will be really helpful.
Thanks, Munna Hossain, Mytechgoal.

First check your on-page status and fix all the issues. Then only your site will be good for offpage seo. Do you know how to do on-page ceck of your site.
There are many tools. Do try to fix all the problems shown in you opage test.
Then it comes to offpage seo.
Add some good quality blog. That depends on you site if needed.
Then start bookmarking, vedio shareing, image sharing etc.

First Plan your keywords with keyword planner.
Complete On page optimization for your website. There are many online tools available to find out your website issues. You can try using this.
Then start with your Off page optimization.
Blog is one of the main factor which drives more user/visitor for your website.

Please follow the below checklinks for any existing website to identify SEO problems -
1. Usability
2. Is it accessible / friendly to search engine spiders
3. Health check using site: yourdomain.com
4. Keyword health check
5. Duplicate content check
6. URL Check - to see it doesn't contain any underscores. Ensure to use keywords in URL.
7. Title Tag Review - Should start with Keyword.
8. Content Review - Check for keyword density.
9. Sitemaps file & Robots.txt verification
10. Redirects checks.
11. Internal linking.
12. Geo-location - set this up in Google Webmaster Tools.
13. External linking/ Back-links profile. Remove all bad back-links with Google disavow tool.
14. Page Speed/ Page load time
15. Check whether the images have Alt tags
16. Error free coding.

For a new website, you should first make sure that your website content is optimized. The process is known as on-page optimization of SEO and requires technical expertise to implement. Blogs, articles, press releases are a part of off-page optimization and involve creating relevant content. You must then use the correct Meta Description and Meta Tags as well. These help the search engines look for topics/keywords and phrases that define your page.

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SEO Checklist plotted below :
1. Equipped CMS
2. Responsive site
3. 301 & 302 Redirects
4. Test website & server load
5. Install SSL
6. Upload sitemap.xml
7. Upload robot.txt file
8. Check broken links
9. Install Google Analytics
10. Content Optimization