Why would you want an LLC?
If these loans are going to be treated as actual loans, you may pay interest to your relatives. That's doesn't affect your tax but they will pay income tax on the interest received. However, you can't deduct the interest as mortgage interest on schedule A unless the loans are "perfected" against the home -- listed as liens against the property with the county clerks office. (You can still deduct the part of interest that is a rental expense against the rental income if you pay interest, even if it isn't perfected.)
Loans are not taxable income to the borrower unless canceled. But in this case, the IRS would probably treat the money as a family gift, unless your relatives are really insistent on making this a business-like loan that is recorded against the home, with interest, etc.
Your cost basis is the amount you actually pay to build the house. It doesnt matter if that amount includes loans or gifts from your relatives, you are still spending "your money" (either a loan you will repay, or a gift) so it counts toward the cost basis.
