Tune your carb. Instructions in the Engine section here.
Check you have good connections from the battery to the starter and from the engine to chassis. Low voltages can cause a weak spark that will struggle with a cold engine. Check you have a clean contact from distributor body to engine and if you have electronic ignition check the orange box is grounded. If you have contact points check they are set right and the rotor and cap are clean and in good condition. Check the coil connections and make sure the coil is clean. Check the spark plug leads, etc etc etc.
Electrical instructions are in the 'electrical' section.
Basically if you don't keep on top of things they can add together and cause bad starting and poor idle etc.
Start with the carb though. Buying a new one may fix it but the chances of it being
exactly right for your engine are slim. However this is what most people do so they don't have to use their brains.
Tuning or re-building your existing carb might teach you a few things about it you didn't know and it will cost a lot less. Everything you need to know about tuning carbs is 'out there' in books or on this message board.
Give it a go and see what happens. You can always go back to plan A and get a new carb if it all goes horribly wrong!