A good contractor will always be able to produce an estimate that is computer generated, send you an email copy, and detail the work to be done.  Would a handwritten estimate scribbled on paper hold up in court?   You should be able to find their company online.  There should be reviews and at least a website.

A good contractor will be insured and bonded.  What does that mean?  General Liability insurance protects you and the contractor from expenses that occur due to accidents in your home due to the contractor's work.  No, it does not protect you from shoddy work.  Bonding is a guarantee that a job will be finished and that it is done correctly and nothing could be stolen from your house.  Bonding is also known as a surety instrument that gives certain guarantees on behalf of a contractor.  It works like a bond to get out of jail. The bond guarantees certain items will be taken care of.  

Let's talk about licensing.   In Texas, you do not need a license to perform most remodeling jobs.  Licenses are required for major electrical, plumbing, and HVAC work.  A general contractor has to be licensed because they perform these tasks as part of a big remodel project. They should hold a license for these types of items.  Major work is a tricky thing.  For example, you can hire a handyman to install a light fixture but moving an electrical plug or rewiring your home requires the skill of an electrician to make sure the repair is up to code.  Anyone who claims to be licensed should be able to provide proof.  Ask for it.  Experience is a big plus.  Most legitimate contractors have many years of experience and have gone to training and research industry standards.  If a contractor does not know industry standards then they probably won't be able to do the work up to industry standards.  Industry standards enable the products you install to last over time.  Would you visit a dentist for a heart problem?

Let's talk about payments.  A good contractor that has a legitimate business will be able to take a credit card.  These days all you need to take credit cards is a business checking account.  There are tons of credit card processors available for small business owners today.  Even PayPal is an option.  Cash is not safe.  Most businesses that do jobs that might take longer than a day or two will require a deposit.  A credit card payment for a deposit will give you the backing of a credit card company's assistance to resolve any issues you might have.  Once you initiate a dispute with your credit card company that money is taken away from the vendor immediately and the vendor has the burden of proof for the legitimacy of the transaction.