If you can stay within one market such that your various websites or products make sense as a whole to your Customers, start one company.
However, if you cannot bring those products/websites together without creating an incongruency in the mind of your Customer, I would opt initially for a DBA (Doing Business As) and second website.
**Update in response to your comment**
Your DBA is not getting funded, your idea is. The DBA is simply "attached" to your existing business entity (your corp or llc) to minimize confusion in the minds of your prospective Customers.
For example, with a DBA you can go to your bank and add that DBA on to your bank account (some banks allow only one, some more than one).
Then you can set up Merchant Processing under the DBA name such that when a Customer orders from your DBA (say, www.mygreatacademiclearningwebsite.com), that DBA is what appears on their monthly credit card statement (or online when they check their account online).
That has nothing to do with risk or funding.
Keep in mind that while minimizing chargebacks, you will increase accounting tasks and monthly expenses with every new merchant account you create.
Another option (instead of creating multiple DBA's and multiple merchant accounts) is to make the statement, "Your credit card statement will reflect a charge from Great Academic Instruction, Inc. (or whatever your corporate name is).
Then put that statement here:
(1) On the "Welcome page" and in the "Welcome" email when ppl sign up for an account on your site.
(2) On the "Thank You" page and "Thank You" email when they purchase.
(3) On the Paid Invoice you send them after they purchase.
Also, give thought to adding something like this at the bottom of emails:
www.XXXXXXX.com is a Great Academic Instruction website. (Or whatever the name of your business is).
When you do set up your Merchant account, make sure your telephone number appears on your Customer's statement next to your business name or dba. People forget. Or, the folks who purchased aren't the folks paying the credit card charge and they cannot make the connection between some new service and your charge. Give them a telephone number they can call and you will save yourself time and money!
Finally, consider that there is a limit to the number of characters available on a Customer's credit card statement - so if you want your entire business name and telephone number to appear, think small!