ATM options are always more liquid. Options with shorter maturities are also more liquid. Best way to learn more is to open a brokerage account that doesn't have any minimum amounts or monthly fees and you can watch some delayed live option quotes across a whole chain of strikes and maturities .
The first question you are asking is really how to profit if the actual drift is considerably different from the risk-free rate.
Here's one good vanilla way - buy call (put) if the actual drift is considerably higher (lower) with the following properties : long maturity (e.g. Leaps) so that the theta decay is small, always either deep OTM or deep ITM so that the option is minimally affected by vega. The choice of deep OTM vs deep ITM is a personal one, because in deep OTM the break even profit may not be reached and you can lose 100% of premium, while in deep ITM, the leverage (gearing) you can get is low and the profits can be much subdued. In practice, since this strategy will be operating at longer maturities and away from the ATM - you will be operating in the illiquid part of the option surface. So to minimize the option bid-ask, from practical experience, you really have to limit yourself to underlying that trade > 5 millions shares / day and the price of underlying should be > 20 if you want to buy puts or <40 if you want to buy calls .
This is a vanilla trade construction. You can always explore more complicated structures. The best structures I have found are OTC options on multiple equity indices (max/min of 3 asset returns, etc.,) if you have a drift view on 3 similar equity indices and a lot of big brokers will quote you max/min of N asset options on super liquid underlyings, or OTC average price options (TAPOs) in the case of commodities which are usually not that liquid.