I'm not sure what you mean about proposing that artists propose their paintings, etc. Do you intend that you act as the artists' agent in selling their works? if so you need to contract with them for that.
You need more of a background in the art business, and in business in general. Yes, you should form a corporation or LLC to provide a liability shield for your personal assets, and it's not something you do at city hall, and yes you have to capitalize this company. You also should done a trademark search before choosing a domain name, to see if the name infringes on anyone's rights, and the webpages themselves can be copyrighted.
Please see the DIY guides linked below if you want to DIY, but your query sounds like you're inexperienced, and you may want to hire a business lawyer for help.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
You should get a business license in the city in which you will be doing business. You should also talk to the county clerk for your county and determine if you need anything else with your county. If you aren't using your last name in your business name, you will also need a fictitious business license. You can start the process with your county. You will need to have the notice published in a local newspaper for four weeks and then show proof of publication to the county. Choose the cheapest local paper you can find for this as this can be expensive.
Your questions raise many issues. I will address a few of them here.
The website would not be a company, but you would do well to form a business entity, either a corporation or a limited liability company, to shield you fro personal liability - please see the first link below.
There is no specified minimum investment, but if the entity is to protect you from personal liability, it must not be severely undercapitalized - please see the second link below.
You should apply for a business license in the city where you will be operating your business.
If you will be operating under a fictitious business name (colloquially, a "DBA"), you should apply to the County Clerk within 40 days of when you first use the name - please see the third link below.
Disclaimer: This post does not constitute legal advice and does not establish an attorney-client relationship.
All of the above answers provide a great deal of information and should help you get started. I thought I would jump in on a couple of housekeeping issues that may shed some light on your question. Please understand that this question regularly comes up in my practice and I usually like to start off with the basics.
First of all, a website is not a business. It may serve a business purpose, but by itself, it is not a business. It also does not entitle you to blanket protection of your brand or trademark (in the event that you wish to pursue this later). I have heard many clients believe that they are entitled to certain business and other legal protections "because I have the website." This analysis does not always hold true. Regularly, it does not.
The best process to set up your business is a simple process. First, form your business in your local county and, if you are unsure of how to do this, consult a local business attorney to assist you with this process. They will assist you in determining what is right for you and your company. They may also assist you with the related tax implications and other regulatory concerns that you might have.
Second, as stated above, before you begin to sell property belonging to other persons, you should contract with them - in the name of the business. You attorney should be able to assist you with this process as well.
THESE COMMENTS MUST NOT BE CONSIDERED LEGAL ADVICE. Comments made on websites such as Avvo.com are provided for informational purposes only. The only way to determine whether how the law may apply to your particular situation is to consult with an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.