If I use the starting wealth rolls of my class, do I keep any remaining money left over after I buy equipment?
In D&D 5e you can roll the 4d4 × 10 to determine starting gold, forgoing any equipment your class and background gets. This is not up for question. What is up for question is whether or not the PC keeps any remaining gold that they don't spend on equipment. As far as I have been able to tell, this is not explicitly stated in the PHB nor in the Basic Rules documents.