Character of service is the block that matters most broadly: most VA benefits require a discharge characterized as honorable, or under honorable conditions for a general discharge. A discharge characterized as other than honorable, bad conduct, or dishonorable narrows what's available and adds complexity, though it doesn't automatically disqualify you from everything. The narrative reason for separation and the associated separation code often travel alongside that characterization, and together they're what a benefits office or state agency will actually check before approving anything.
If your DD-214 shows a characterization other than honorable, it's worth understanding your options rather than assuming the door is closed. Discharge upgrades are a real, if not guaranteed, process through your service branch's Discharge Review Board or Board for Correction of Military or Naval Records, and circumstances connected to trauma, mental health conditions, or sexual assault experienced during service are increasingly considered relevant to those boards. The process takes time and typically benefits from supporting documentation, so it's worth starting well before you need the upgrade for a specific benefit application. The Discharge Upgrade Checker walks through eligibility factors and the general process for requesting a review.