We always advise our clients to work through the claims process and obtain as much money possible on your own before having an attorney review your file for a potential lawsuit. Your insurance company will make an initial offer which is negotiable. If you feel the offer is unfair, you have every right to challenge it.
Once you believe you have gone as far as you can go yet you still believe you are being unfairly compensated, then seek legal advice. In my experiences we can usually tell a client after an initial meeting if we believe we can obtain more money on their behalf. In almost all of our lawsuits, we've been able to obtain significantly more money than the insurance company's "last, best offer" to the client.
You can expect to pay a contingent fee in the 40% range in a lawsuit against your insurance company. You will also be responsible for costs including expert fees out of whatever result might be obtained on your behalf. Understand that it is not a quick process but, litigation can be a productive, though last resort to obtain what you are owed.