How do I increase DA and PA for my domain name? How SEO will be beneficial with DA or PA?

You can check Moz Authority first.

Steps to increase Domain Authority

1. Your domain name matter the most, choose a domain name where you can get “Word of mouth” publicity. So choose it wisely.
2. You need to get many backlinks from good domains.
3. Your website should load in 3 seconds.
4. Add guest posting on a good website with an 18+ score of DA.
5. Low-quality backlinks will put your website's reputation down!

Steps to increase Page Authority

1. Create great and unique content for your website, search engines avoid existing or duplicate ones!
2. Promote your content with email, social media, and direct links to your friends and family.
3. Optimize your fonts, headers, subheaders and do the on-page SEO.
4. Increase readability for your website visitors.
5. Optimize keywords that users are typing in the search engines like google, bing, Yandex, etc.
6. Add internal links to your website. Add "you may like" posts after each article.
7. Don't add bad links to your article at all. It will put down your website reputation.
8. Make your pages mobile-friendly.
9. Be consistent while writing the article.

As per your question about On-page or off-page SEO:

Both are important from my perspective!

You can make a checklist to increase your website popularity:

1. Check disallow rules in your robots.txt - it will tell about your website to google bots, Yandex bots, and bing bots regarding what's inside your pages?
2. Check no-index tags from your search console, remove the page if any exist.
3. Check your sitemap and submit it to different search engine giants.
4. Set internal links for each article, pointing to another article on your website itself.
5. Check indexing by duplicates and canonical tags
6. Check for soft 404 (In your Index coverage) - try to add unique content to your website.
7. Fix crawl issues if applicable!

Hope this steps will be helpful to achieve your goals.