Hello kph
Regarding Lender's Mortgage Insurance and Low Doc loans, this really depends on the lender and their lending policies.
For example, while most lenders which offer Low Doc loans may not charge the premium to the customer some will do so after, say, 76%LVR.
As a general rule you can expect to not be charged for the premium but many lenders offer discounted interest rates if the borrower pays the premium.
The most recent lo doc which I wrote for myself, I earnt a .25% discount off the rate simply by paying the premium. Money well spent.
'Best Products' are, like beauty, in the eye of the beholder.
Each month brings it's own Special Deals - low or no application fees, discounted rates, some sort of bonus product, whatever - across the range of lenders there will always be a Monthly Special offered somewhere.
What is 'best' for you may not be any temptation to someone else. Sorry, but the most generic statement I could make here is that you could reasonably expect to do better than the Standard Variable (7.32%) on most low doc products on the market at the moment.
Not all lenders will allow low doc for construction, family companies or trusts, but some will in some form or another eg the LVR may be lower than 80%.
At the end of the day it is still the natural person who is borrowing the money and who is guaranteeing the repayment of the loan.
Low doc loans range from any LVR (eg 60%) through to 90%, with or without mortgage insurance, will or won't do construction etc
It really depends more on what you are wanting to achieve in the first place and then the loan to suit you comes later.
Cheers
Kristine