"What is the ideal way to deal with a LLC startup were personal funds are used to pay business expenses?"

The business expenses don't get treated any differently, just because personal funds were put into the business so that the expenses could be paid.

"Should the personal expenses labeled as owner's investment, or should be labeled some type of other expense?"

You don't track personal expenses for business recordkeeping at all. You would track Draws; the owner took funds to be used personally and it does not matter why or on what.