Which is the best SEO tool for a new site?

I have collected six of them, with which you can master the art of SEO and make your site a successful one.

1. Google and Bing:
The Google and Bing are search engines where the functionality works best for mastering the art of SEO. The Google-fu and Bing-fu, are equally good in examining the indexation process and in duplicating content. It also checks the keyword rankings, finds out the content scrapers, analyzes the SERP listings, and outreaches the link prospects.

2. Google Search Console
Google Search Console , formerly known as "Google Webmaster Tools"provides you with data and configuration control for your sites in Google.

3. Google Analytics
Till date, Google Analytics is the most valuable and popular SEO data tool that maintains the record of visitors and their interactions and activities with your site.

4. Moz
SERP_Overlay Moz is a user-friendly suite of inbound marketing tools like:

Followerwonk: This shows data on Twitter.
Moz Local: Shows the state of a company's local citations and the first start of the local SEO on a site.
The SERP Overlay: It is a part of the Mozbar displaying the OSE metrics on individual search results.

5. Google Keyword Planner
Google's Keyword Planner formerly known as Adwords Keyword Tool, pulls up the monthly Google search queries estimating the volume for dozens of keywords in seconds.

6. Screaming Frog
Screaming Frog is actually a website crawler that is particularly designed for SEO. Within mere minutes, they collect the critical data on every URL. The best way to use it is downloading and start using it for a spin.

Here are some of the tools you should check out for your SEO needs.

1. SEMRush : If you are serious about SEO then you should atleast try the demo version of the tool. It has all the features like keyword search, competitor check, domain check and other SEO features. Most likely this is the tool that you need for most common SEO needs of yours. Also this tool can help you improve your SEO objectives (e.g. footprints and on page SEO).
Price : Demo (30 days) and Paid for regular usage.

2. KeywordTool.io : This tool scrapes the keywords from Google (all the regional google sites included), bing, yahoo, ask, youtube and few others. It also exports the keyword into excel or the CSV file. If you need keywords for your titles then this is the tool that you need.
Price (Free for basic, paid for advanced features)

3. SEOBook Tools: This website has some premium level of tools which allow you to do research for keywords, verify the SEO on your own page and few others. The tools are under paid category and the price however is high for someone who is new to the SEO usage.
Price: Paid

4. Keyword Tracker : You may find that the database from the google and bing alone doesn't justify your keyword needs. In such case the keyword tracker is a good option to check into. It has a lot of options to export your searched keyword. The quality of keywords and the ability to sort out the keywords makes this tool really useful.
Price: Paid

Apart from the above mentioned tools there are some free tools or paid tools scattered around for the following usage scenarios:

1. Broken link checker
2. Dofollow link checker
3. Social media reach checker
4. Twitter mention and hashtag tracker
5. Domain name checker
6. Title checker

The above listed usage requires specific tools and those tools often are not found within single software. So you have to find the multiple free or paid tools and use them accordingly.

I'd say first start with on page SEO and then proceed with off page SEO. This way you can understand which tools to use and which tools to skip.

A couple of tools Other than those mentioned above could be helpful in SEO -

1. Bing webmaster tools
It lets you know the Bing searches on your site. It also gives info on crawling, indexation and other elements.

2. Google trends

It shows you the list of trending searches. In fact, it is one of the most overlooked tools. You will be able to keep track of the market trends.

3. Chrome developer tools
The tool lets you examine SEO. You can diagnose page speed.