How to choose from options from house painting company?
I don't really know what cheapest paint vs. thicker paint means.  I am assuming that the cheaper paint is still a good paint if this is a company using it - not just some guy with cheap paint.  So I am making an assumption.  I am also assuming that the three levels all involve the same Day 1 finished look of the house because really if you are paying them they should be doing a professional job on any of the choices.

So:


I would not expect said company to exist in 6 years let alone 14 years.  They could.  But your expectation for this type of company is they won't.  
If said company had a lot of issues with their paint, it would probably be more cost effective to fold and open under a new name.  And if the company does a great job then you probably have no reason to call them back.
It would be very difficult to prove that an issue 5-14 years later was due to the company's installation of the paint.  They will invariably come back with a list of home owner reasons.
You can't expect a company to come out and fix nicks, oily hand marks and so on.  There is wear and tear on paint due to the owner.  If you don't ever touch your walls and the temp/humidity levels in your house are acceptable a good paint will last 20 years easy.  But it doesn't in high traffic areas because we hit the walls with our body, hands, feet, furniture, whatever.
Do you even know if you will be in the house in 15 years?


So yea I would go the cheapo route.  Maybe get a little more information on the paint difference between 1-2 and look up the manufacturer info and reviews for those paints.  If there is a difference I would say slap on paint #2 and keep the warranty at 6 years.  You have to be honest with yourself.  Would you expect anyone to come back and repaint your house anytime after 3-6 months?   

I have used TONS of different painting crews.  I verify while they are painting the exact type of paint.  Most of the time I choose the paint and provide that for them - I think you should ask about this option.  Often they might say well we only use this type of paint - and then be like great I will buy that then, as long as said paint is good.  I then look over their work as they go along and then inspect paint.  On last day I walk around with little bits of blue painters tape and mark any missed spots.  They fix those spots and we are done.  I don't call them back 3 months later if there is a scuff mark on a wall or if something is peeling.  If a week later I notice that they missed something big maybe I call but that is kind of on me - I missed a closet one time (well they did too) and a couple guys came to paint it.  That's it though.  If some guys come paint your house they don't own your wall issues for the next 15 years.