Weight lifting and Cardio program - advice

The one that is more important to you, is the one you want to do first.

Are you looking to burn fat? If so I'd do weights first since you'll be using most if not all your glycogen and cardio after since you'll be using fat as fuel. If you're not aiming for fat loss though...Do whatever appeals to you first.

If you're looking to put in the miles though I'd suggest light cardio on a lifting day and then an actual run on non-lifting days as some people consider running to some degree as a Leg day

Like Johnythan said, it is better to do then separate days, if possible. My busy life makes it easier to do them back to back, plus I've been doing it so long, that it's really not too difficult for me. They say you should do weight lifting first, because the cardio will use up your glycogen stores that your muscles will need for lifting weights. You won't be able to lift as heavy after a cardio session. I feel the difference when I do cardio first, can't lift as heavy, or atleast it seems. If you do them back to back, I would eat something to with some protein and carbs, to get your energy back up, before you do the other thing.

I'm not a fan of doing both in the same session - inevitably whatever you do second is compromised. Alternate days can work well (I mostly do 3 & 3 with one rest day).
If you really want to do both in one session then whichever is your priority you should do first.

I got to my gym yesterday to find it bursting at the seams (is it January by any chance?) and had no choice but to do a 5k run followed by a bits & pieces weights workout. 5k was in shoes only suitable for lifting and my weights were below par as I was tired. All in all pretty much a waste of time and effort and not really enjoyable either.

Weights before cardio. Better yet, weights in the morn and cardio at night.

If you can't split them to separate days, do weights first. You won't have as much energy for your weight training if you do it after your cardio. You'll be able to push yourself through your cardio workout feeling muscle fatigue. I've done it - you can't push yourself in weight training if you're already fatigued by the time you hit the weights.

Don't do both in the same workout. One will cause the other to suffer, and your recovery will be problematic. Focus on strength training and do cardio on other days. Leave 1-2 days a week for rear.

I disagree. You can do both. It's only a problem unless you're a pure strength athlete or competetive athlete.

If you're on an empty stomach in the morning, do cardio first. Drink a quick protein shake or eat a bananna, then start your weight training session. Try not to lift on an empty stomache after cardio in the morning. You'll have 0 energy. Been there, done that.

If you're NOT on an empty stomach, then do weights first. You should feel quite 'fatigued' by the end of your weight training session.(40 min - 1 hour). If you don't, you haven't done weight training properly.

do NOT do long, steady state cardio at the end of your weight training session. Instead, do interval training for 10-15 min.

for example, hop on a stationary bike. warm up for 5 min(medium pace), then 20 second sprint/ 40 seconds slow... repeat 10 times.

Make sure that you are SPRINTING for 20 seconds, not 80% or 90% or 95%. It might not be that hard the first 2-3 times, but after that, it'll be a struggle to go 100%. Try your best.

As you get fitter, try and decrease the 'slow' time so it's 1:1 with sprint/slow.... If that gets easy, TABATA time with only 10 seconds of rest after each sprint.