1. The company itself
Make sure you get (copies of) their company documents (company establishment, license, etc). Visit their office and at least one of their ongoing or previous projects. And you can also do simple research on the internet about their company and their contact (director).
2. Sign a proper agreement with the company directors
When I say proper, it means you must include a timeline, payment scheme, fines or consequences in case of default and the choice of law of either party.
3. Payment terms
Never agree to pay fifty percent upfront. An established construction company will gladly accept a twenty percent deposit and (even) return the deposit according to progress.
4. Precise drawing
Please complete your project with exact drawings with detailed specifications, this will help you and your construction company to be on the same page for project quality.
5. Feel free to hire an independent third party
It could be a lawyer to help you make sure that the terms in your agreement are sufficient and or an architect/quantity surveyor to measure the progress of your project before you make any further payments.