There are various "endorsements" available for CDL holders, to be able to haul different freight like tank trucks and hazardous materials.
The endorsements will require a separate test for each, and you can usually take them at the same time as your permit test, for a small additional fee.
The rules for when you can take the Hazmat test vary by state, but keep in mind that a TSA background check will have to be approved before you can get the actual endorsement, which usually takes around 30 days.
Simply put, you should get all endorsements that are available. It will open up more opportunities down the line for the types of cargo you can haul.
Again, having the Hazmat and TWIC will make you available for more opportunities when it comes to hauling freight.
Additionally, many trucking companies will require you to have them, either as a condition of hire or by requiring you to get them in a certain time frame afterwards.
Various restrictions can be placed on your CDL, for things such as not taking the skills test in a vehicle equipped with an automatic transmission, taking the test in a lower class vehicle, or not passing the Air Brakes knowledge exam.
We will always recommend that new drivers go for the Class A license, with all endorsements, and take the exam in a truck with a manual transmission. There are no reasons NOT to do these things, and will help you in the long run.