There is no standard royalty for what you describe.
Further, your facts are not just a "normal" web design" but an integral part of your whole business model. I really suspect you would benefit from a consultation with a business attorney in the industry to discuss your business model, your form for doing business, protection of your IP, and a written agreement between you an your investment "partner".
The above is general legal and business analysis. It is not "legal advice" but analysis, and different lawyers may analyse this matter differently, especially if there are additional facts not reflected in the question. I am not your attorney until retained by a written retainer agreement signed by both of us. I am only licensed in California. See also avvo.com terms and conditions item 9, incorporated as if it was reprinted here.
No, nothing is paper, legally speaking until you have a written agreement. You as the creator, are the author and automatically have copyright protection unless you sign it away. Even though you own the copyright protection if there is not written agreement, that does not prevent the company from getting an implicit license to use it, particularly if they are paying for it and it appears intended that they use it. You said they will be doing the promotion, but "promotion" is a vague term. You need to have this all spelled out in a written agreement so what you get and they get and what you pay in royalties is set so there is no valid dispute later. A written agreement keeps them (and You) honest. Now is the time to get it while you need each other. Later on one of you will want to restructure the deal, and if you don't have this in writing it may be the one with the gold that makes the rules, which appears to be them.
The attorney you need is called an Internet attorney or Business Attorney or better yet, an Internet Business Attorney. Some IP attorneys can also do such agreements.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
I agree with my colleagues. If you have no written agreement, you need to look at the terms described in your emails with an attorney. Then you need to devise an agreement before you finish the work. I can imagine the possibility that you will need their permission to put copyrighted material regarding their products on the site. In other words, you may both need each other and you both need an agreement both ways regarding what the terms of your agreement.
You really need an attorney to fully review your matter and assist you to prepare a written agreement regarding the terms.
Providing this answer does not form an attorney-client relationship. Most legal questions are exceedingly fact-sensitive and therefore this answer is a best-guess based on the information you provide. You should consult an attorney licensed in your state to further discuss your matter.
There is no right or wrong answer, and no standard royalty. This is the subject of negotiation between you and the company that is paying to create the web-site.
But I am worried about your situation. It sounds like you are already putting a lot of time and effort into this without having a written agreement in place with the company that is financing your work. This is a huge mistake---and potentially dangerous. Frankly, it would have been wise for you to retain counsel to draft such agreement before you entered into a relationship with this company. In any event, it is critical that you retain counsel to draft and negotiate such an agreement---do not wait until you finish your work because your leverage in the negotiation will be low. The time to retain counsel and negotiate this deal is now.