@Ronald Cooperman You don't specify what data you're looking for from listsource, what don't they have? As for your letter, here are some thoughts...
Children moved out- This won't apply to the majority of people on your list so it will seem a lot less personable.
Have some bills that you need to address- People get offended at the suggestion of being behind on bills, even if they actually are behind on bills. Stay away from insinuating people are financially stressed.
House needs a new heater or kitchen- This is too specific, what if the house needs a new roof, paint, bathrooms, flooring? I would say "Does the house need some repairs or updating?"
People want brand new appliances, new floors updated bathrooms and kitchens- I would remove this entirely.
If you don’t want to be bothered updating or the money call us- "If you want a quick, hassle free transaction, then give us a call!"
Leave all the problems to us.- Don't suggest "problems", it will insult some people. Instead, write "We buy houses as-is, meaning you don't have to make any repairs, if needed."
We pay cash settle quick no commissions or fees- "We pay cash so we can close quickly and you don't pay any fees."
What do you have to lose- "Call us for a free, no obligation, cash offer to see if we might be a great option for you"