First, I must point out that it would be somewhat odd to choose a state to incorporate in based on the cost of share authorization, as the number of authorized shares typically does not have much of an effect apart from the psychological difference of receiving more shares. Obviously, what is of much greater consequence is the number of shares one is issued relative to the total outstanding shares of the corporation (i.e., 20 of 100 shares is essentially the same as 20,000,000 of 100,000,000 shares).
With that in mind, to answer your question, yes, you can issue yourself 20,000,000 shares, or any number you please, in a newly-formed DE corporation. In doing so, you may subject yourself to taxes, the amount of which being determined by a number of factors, including whether or not the company is issuing shares with no par value or a par value. Generally, if you issue 5,000 shares or less you don't really need to worry about these calculations, but if more than that number is issued, you will need to be careful in determining whether or not you want to use par value or no par value shares, what par values you should use, etc. These calculations can be confusing if you are not familiar with the process, and you should be careful in doing so, as you can create significant annual tax obligations if you do not understand the process. However, if you do want to issue a high number of shares, its usually best to use par value stock with a very low stated par value (as low as $0.000001) to minimize your tax obligations. So in short, yes there may be a cost in authorizing 25,000,000 shares in DE. However, issuing millions of shares in NY has a similar set of issues, only it uses a totally different formula and set of rules to calculate taxes for corporations issuing more than 200 shares. Both the websites for the DE and NY Secretaries of State contain explanations of these rules and calculations, but as stated above, they can be somewhat confusing, and great care should be taken to avoid inadvertently subjecting yourself to unnecessarily high annual taxes based upon authorized shares.
Due to the complexity of these rules, I suggest that you contact an attorney to advise you on this if you have any uncertainties. In reality, having an attorney organize your corporation is probably the best course to take, as they will help you to determine the best entity type, state to organize in, number of shares to authorize, and then helping you to properly draft and file organizational documents such as articles of incorporation and corporate bylaws. The cost of doing so should not be great, and the benefits of doing so should outweigh such costs.
This advice is for INFORMATIONAL PURPOSES only and should not be relied upon as legal advice. No attorney-client relationship shall be formed as a result of the answer above.
I agree with the previous answer, and I would point out an additional question you should answer:
Why do you need to issue yourself 20 million shares? It seems that your concern here is potentially losing control of the corporation if it is a success. This is a matter that can be handled through the manner of incorporation or business formation instead of control-of-shares. For that matter, you might reconsider why you want to incorporate at all as a corporation, rather than some other business form like a limited partnership. You should consult a business formation attorney to discuss these issues.
This does not constitute legal advice or the engagement of my services as an attorney.