Macro financial data is out there available to the public but is a tremendous pain to gather all of this and do your analysis. That is why you see services that charge money so you can get it all in one platform in a neat format. There are literally hundreds of data to gather. My suggestion would be to subscribe https://www.businesscycle.com/6 for few months and see what they gather and the sources they use then do it yourself.
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Hard to tell what it is you are looking for, equity data, macro data, legal data?
A lot if it is public and you basically just need to search the official websites (SEC,FRED, IMF, ECB, CDC...). For US-equities some websites have lots of financial data built-in, check www.koyfin.com6 and Tikr (Referral link; https://app.tikr.com/register?ref=q5pfta5).
For alternative data there is https://www.quandl.com/6
Here is a fun AUM tracker; https://aum13f.com/6
I would second @Seth Dingle2 suggestions although personally I don't use barchart, the other two definitely.
Although not for extracting and manipulating, but access to Bloombergesque data I can highly recommend Koyfin. Most other data sites concentrate on equities. Koyfin has that plus rates, commodities, currencies etc globally not just US centric. Also you can build your own dashboard for quick looks.
As you highlighted regards data access. If you are charging someone 2&20 to invest their money you can't be making decisions based on data the plebs can access ;) Many use proprietary data gained from source.
Here are a few free resources to get started. FRED and BIS is for economic data, Barchart Is a FREE market data/charting software where you can apply some technical studies easily. To see how to blend some fundamental and technical analysis I would highly suggest checking out @Christopher Moir1 his latest post on gold vs oil (https://exchange.realvision.com/post/what-do-gold-miners-need-in-order-to-mine-gold-6000338aac6848f87f866ce12 ) is a great example solid research. Also @Weston Nakamura3 who routinely posts research pieces of exceptional thoughtfulness and depth. Find a piece of research that resonates with you and try to recreate it using the sources I linked or others.