Weight lifting can be as beneficial as cardio for losing weight, so there is no reason to choose one or the other - do both.
I think the most important thing if you want to lose LOTS of weight, is firstly not to set your targets too high. Come up with a training schedule that you will stick to long-term, rather than a really intense program that you give up after a few weeks.
Once you get used to the schedule, work on gradually increasing the difficulty - lifting slightly heavier weights, running (or cycling) harder or longer. Over time you should see the weight come down, though be aware that gaining muscle (which is inevitable when doing weights OR cardio) will limit your weight loss - don't focus on the scales as much as how you
look and
feel.
You also need to keep your diet in check. I imagine at 307lbs that you eat a fair amount of calories each day. Again the trick is to
gradually reduce this, rather than suddenly eating very little (this can cause your body to store more fat as a 'starvation response' to you eating too little). Try and cut down on fast food, and anything with lots of sugar.
If you are dedicated to losing the weight, then have self-belief that it *will* happen, but it does take time and effort.