Cardio or Weights First?
Well, the short answer is that weights should come before cardio.
The long answer is: It depends on what you're trying to achieve.
The reason why I suggest doing weights first is that you want to perform weights at your best and most energized state. Not to mention, you have tons of carbs (glycogen) stored up that will fuel your workout. Weights help build lean muscle therefore will lead you to get stronger and leaner, and cardio can come second in order to burn off some additional calories as well as stored fat once you burn through your carbohydrates. You get the best of both worlds this way.
But, I also say it depends because not everyone is trying to achieve the same thing.
If you're training for an endurance event or race:
Cardio first - build up your endurance and stamina, then you can add weights for strength.
If you're close to your goal weight but want to "tone":
Weights first - and don't be afraid to lift heavy! If you're new to weights, start with body weight exercises and gradually increase your weights, but do not increase them too quickly. I suggest increasing your weight only once every 3-4 weeks.
If you want to lose a large amount of weight:
Try to alternate your focus days. If you're going to the gym four days a week, make two of them cardio-led and the other two strength-led, or three cardio and one strength, etc. That way you are burning the Calories you need to create a deficit and lose weight, but building muscle helps you to burn Calories when you're NOT working out, and will help you tighten your body as well as see and feel changes in the way you look (as opposed to watching the number on the scale).
If you want to build muscle:
Well, this one should be obvious - strength first.
If you want to maintain your current physique or make gradual changes without anything too significant:
Do whichever you dislike first, that way you can end your workout with something you enjoy.
I personally have done both - I used to perform cardio before weights while I was training for my 5K, but then switched to doing weights before cardio, and I prefer saving cardio for last so that I don't have to walk around in a sweaty outfit afterwards. There's no right answer for this, but choose what works best for your goals and your body.