Below is a simple, typical SEO Company’s checklist for On-Page optimisation. In brackets denotes their importance.
Page titles (Vital)
The <title> tag should contain your most important keywords and they should be placed at the beginning of the tag. Keep it short and simple. Do not stuff with keywords. Less than 60-70 characters.
Description and Keywords Meta Tags (Fairly important)
With respect to Google, the Description and Keywords Meta Tags can be ignored. Best practice is to fill in the Description tag to grab the visitor’s attention. The Keywords tag is useful for other search engines and social bookmarking sites, keep these short, no more than 10 words.
Heading tags (Fairly important)
Where possible, include only one H1 tag per page. H1s should be short and simple, containing your main keyword in a phrase. Use secondary keywords in H2, H3 tags, etc.
Unique content (Very important)
Search engines prefer to index unique content. Not having unique copy usually results in search engines going elsewhere.
Synonyms and phrase variance (Fairly important)
Use a thesaurus to find similar words. Singularise/pluralise keywords. Use your keywords differently than you would normally do for phrase variance.
Keyword density (Fairly important)
Be natural with your keyword phrases and avoid keyword stuffing. Use synonyms and variance in your phrasing, as above. Make sure target keywords are in the first couple paragraphs, at least above the fold.
Spelling and grammar (Fairly important)
Intelligible, well-written copy not only serves the likes of Google but visitors will appreciate the content as well.
Semantic markup (Fairly important)
Use html code with meaning where possible. For example, place meaningful headings in H1 and H2 tags, use tables for tabular data. See semantic markup.
Clean markup (Fairly important)
Clean code up where possible. Unnecessary markup leads to larger file sizes and can sometimes throw off search engines. Clean and semantic code has a better success rate in displaying on most devices.
Emphasise keywords (Fairly important)
Use tags such as <strong> around your keyword phrases. Use sparingly.
Naming conventions (Fairly important)
Check file names are relevant and they contain related keyword terms (this applies to images, videos, PDFs and docs as well). If possible, avoid using a system which requires using IDs and parameters for loading up a resource.
Optimise images (Fairly important)
Optimise images towards smaller file sizes. Make sure <img> alt attributes are filled in with short, simple relevant phrases related to the image.
Site integrity (Very important)
Use software such as Screaming Frog SEO Spider to check the header status codes coming from your site to find inconsistencies such as broken links and images. Update/remove any inconsistencies. Resources should have a single hop to a 200OK status; permanent redirects should have a 301 to the correct location; and broken links and images will give a 404 File Not Found so should be updated or removed from the offending resource.
Site speed (Fairly important)
Make sure site is optimised for speed where possible. See page-speed optimisation.
Webmaster Tools (Very important)
Further to site integrity, signup/check Google’s Webmaster Tools to see if any errors/inconsistencies are reported.
Anchor text (Fairly important)
Check anchor text in your links across the site are well optimised, meaningful, and contains a good proportion of keywords related to the page. See contextual linking in SEO.
Robots.txt (Fairly important)
Make sure to block any files/pages which you do not wish to be crawled. Verify the robots.txt file is working as intended.
XML sitemap (Fairly important)
Submit XML sitemaps to Webmaster Tools. For larger sites with 100+ pages break them up into meaningful chunks such as by category and submit.