As long as your car is moving, it won't stall. How exactly are you taking off from a stand still? Assuming that there's a relatively healthy clutch/flywheel in your car, are you...
1. Reving the engine high and then dropping the clutch aggressively (meaning just a clutch pedel let go at high RPM) and while at the same time letting your foot off the gas as you drop the clutch?
2. Reving the engine to around 1K to 1.5K RPM and letting the clutch go while doing the same thing as 1 (ie. not keeping the gas down).
3. Keeping RPMs around 1K to 1.5K while sliding in the clutch and slowly applying more throttle.
In some cases, situations 1 and 2 will cause the car to stall because there isn't a continuous amount of RPM. Because your car is on a standstill, and it's quite heavy, dropping the clutch without a continuous throttle delivery, isn't enough power to get the car to move sufficiently enough to keep engine speeds from dipping below 500 RPM. Although there is a sudden jolt, the weight, drag, and sudden loss of power will contribute to a stall.
You don't have to rev your engine to high RPM to get it off a still. Just keep your foot on the throttle to around 1 to 1.5K RPM and slowly let go of the clutch. As the clutch catches the flywheel, your engine speeds will dip slightly. Try to maintain > 1K RPM and you should get your car moving smoothly, without jerk and avoid random stalling. Don't shoot for >2.5/3K RPM or you risk wearing the clutch faster and you'll cause a yank motion on your car (unless you want that).
Also, considering that you said you have high mileage on your car, how high is high exactly? And if you haven't had the clutch assembly replaced in a few years, I would definitely check the state of its health out at this point. Your stalling could be that the clutch is slipping - not enough clutch grip and slides on the flywheel - and as you let go of the throttle thinking that the clutch is engaged, it may infact be slipping and when it does engage, you no longer have enough engine speed and the car stalls.