Q: Car doesn't turn over right away sometimes

A slight delay by the starter like this is often a bad high current connection somewhere along the power path from the battery to the starter. It literally can take a second or three for battery power to overcome corrosion, or a poor physical connection. A confirmation of this diagnosis would be - when the starter does kick off, does it sound like it’s turning the engine over slower than it should be? If so, this confirms the problem. A bad high current connection can be where the battery connects to the cables, the battery cable connections to both the engine ground and the starter respectively, poor ground connectivity between the engine and the chassis, burned contacts in the starter solenoid, and worn brushes in the starter motor itself. It is possible also that the ignition "start" trigger path, which runs through the ignition switch (possible burned contacts), and triggers the starter solenoid, may also have poor connectivity along the way. I would recommend having an Car Will Not Start Inspection completed by a mobile, professional mechanic, such as one from YourMechanic, to diagnose this problem, get an accurate assessment of damage and cost estimate for repairs.