YJSwan

In addition to what GeorgiaTechPhd said, you can be very honest with the professors about your options. They know how the admission process works and understand that everyone wants to wait for the best option. You can even share with them which schools you're waiting for.
One of my professors in grad school emailed with an admitted applicants multiple times. The professor helped him with scholarship and everything. Then the applicant was a little embarrassed to tell the professor he just got admitted into another school. My professor said to him, "Why are you even hesitating? That's a good school. Reject this one and accept the other before time runs out." He was truly happy for that applicant and we lost a great candidate to a better school. The moral of the story is that good professors always have the best interest of students at heart. They don't get offended just because you want the best result.
And, if someone does get offended just because you want the best result for your life, it may as well serve as a warning that they may not be good advisors anyway... 
Courtesy and honesty. These two can never go wrong. 

I think, as a general rule for most official situations, it is always good to be communicative rather than not being responsive. The only catch is that you need to be polite and considerate, and not just end up saying whatever you are thinking. 

In the specific situation that you have mentioned, I would definitely reach out to the faculty member -- thank them for the offer, and even talk to them to understand more about their work, the environment, and the expectations. The more information you have the easier it will be for you to decide later on. Even if you think that you have all the answers, and there is nothing more you want to know, you should still reach out -- thank them, reiterate your interest, and politely let them know that its a big decision for you, so you don't want to hurry into it and consider all possible factors. And let them know that you will reach out to them in case you have any more questions to ask. 

Remember that this person might be your advisor one day, so you definitely want to maintain a good relation with them, and the first step to that is establishing a good communication channel.