|Normally, the correct oil is the same as is used in the engine -- 10W40 or 20W50 depending on the ambient temperature. This works quite well for the average car under normal conditions.
If conditions are not average, experiment until you find the fluid that gives best results when the throttle is suddenly opened under load. The best way to make this determination is to use a fuel / air mixture meter during your tests, but if necessary you can 'tune by ear' and by feel. If the transient fuel/air mix is too lean, you'll want a more viscous fluid (heavier oil). If the transient fuel/air mix is too rich, you'll want a less viscous fluid (lighter oil). If in doubt, always go for the heavier oil.
CAUTION: do not use any fluid that absorbs water or your carbs will eventually be utterly destroyed by rust.
As for how much oil to use, when the plastic cap-and-damper assembly atop the carb is unscrewed and removed, you'll see the hollow top of the vacuum valve sitting down in the bore thus revealed. Just fill the hollow part of the valve (not the entire bore) until the oil approaches the top -- it's not critical, as any excess fluid will eventually be sucked into the engine and consumed -- then reinstall the cap-and-damper assembly. You should notice some resistance to this reinstallation while the cap is still well above the body of the carburetor; if not, add more oil.
The oil level should remain constant indefinitely, though in practice you may need to top up the oil every month or when filling the fuel tank. If the oil is consumed at a more rapid rate, the o-ring that seals the mixture needle adjuster is worn out and needs replacement. This is a standard size (AS568A-010) o-ring made from nitrile rubber or the rather more expensive viton rubber, and should be available from any decent hardware store, Delta Motorsports (O19657), Moss (365-420), as well as in the standard carb rebuild kit.
If you need to replace one of these o-rings, you might as well do both of them, as it will be necessary to re-adjust the fuel mixture setting, and probably the balance, on the car's carburetors.