Which is more important the price or implied volatility? A stk has all the indicator that the future 1 month movement would not move alot and you want to use some strategies to profit from the lack of movement but the implied volatility is at new low and change of implied volatility would dampen the profit. Would you go for the trade?

Whenever you use a term like "would not move alot", you must be comparing it to something. If you're comparing versus current implied volatility, if you are stating that a stock is likely to be less volatile than implied volatility, then that's a world-view that can be traded: by selling volatility (using any number of strategies). If you're selling front-month options and you're going to hold until expiration anyways, then you don't care how implied volatility is going to move in the interim.

realized volatility less than implied volatility do not imply that implied volatility would fall and selling options is good strategy. Both realized volatility and implied volatility would be more and would dampen profit

Uh, no. If you know realized volatility (from now until expiration) will be less than implied volatility (now), then in a BS world, you are guaranteed a profit by selling options and delta hedging until expiration. Future implied volatility does not matter.

are you saying that implied volatility higher than the implied volatility at opening trade would not dampen profit from selling options?

Future implied volatility only matters if you plan on trading out of your option position. If you're holding your position indefinitely (until expiration) and only trading underlying, then future implied volatility doesn't matter.

If you're short, IV may affect your margin but as heech suggested, its variations are fairly irrelevant if you're holding to exp.

So what? In this scenario you're holding to expiration. When you hedge, you calculate delta based on your "known" future realized volatility (which guarantees a profit if true). The current market value of options, ie implied volatility, is totally irrelevant since you're never trading them after initial entry.