A warm up should be something that gets your hear rate elevated, gets you ready to do your planned work out effectively and safely, and isn't so long that it tires you out or bores you. Also, IMO, it should be something fairly enjoyable so you look forward to getting to the gym. Don't over think it.
Options I like (keep it 5-7 minutes long, in total. Make sure you're remaining fresh for your work out)
Jumping jacks (2-3 minutes), leg swings, arm circles, bodyweight exercises (NOT high volume).
Jump rope, shadow boxing, dynamic stretching.
Vinyasa-style yoga, row machine,
Foam rolling, band pull aparts, dynamic stretching