If you know you’ll be coming to a complete stop fairly abruptly (e.g. at a stop sign), then there’s no need to shift down through the gears letting the clutch out each time. In fact, as you’ve found, it can be counter-productive.
When you’re approaching the stop sign or whatever, just pull in the clutch, holding it there, and click, click, click down through the gears while braking, until you get into first gear just before you stop.
Then you can either hold it there in first gear with the clutch still pulled-in (e.g. at a stop sign) or you can put it into neutral and let out the clutch once you’ve stopped (e.g. at a traffic light).
Some people advise to always keep it in first gear with the clutch pulled-in at a stop. That’s so that you can quickly get out of the way if a madman in another vehicle is approaching too rapidly from behind and looks like he might ram into you.
For traffic lights, you can modify this slightly because the light might change to green during your approach.
So! For red traffic lights, do as above, but instead of just click, click, clicking down through all the gears one immediately after the other, instead, hold in the clutch for the duration of your slow-down (as above), but only click down into the next lower gear when you have slowed to a speed which is appropriate for that lower gear (you’re also braking at the same time remember). That way, if the light changes to green at any time during your slowing down phase, you’ll be in the correct gear to proceed, in which case, you just let off the brakes and slowly let out the clutch as you give it a little throttle. Voila!