Welcome to CC.
The project your making will dictate (to an extent) what kind of cake you'll want to use. As stated above by MFD, a more dense cake will work better for carving, for example.
Generally, if you have a proper, internal support structure you can use whatever recipe you want as long as it can hold the weight of the icing and fondant. And there's personal preference, I enjoy working with (and eating) mudcake, you'll need to experiment and find something that works for you.
Your first question, yes, typically the same icing used for your crumb coat is used for your final coat, then fondant if using. The crumb coat is a great step for beginners, it's supposed to be a very thin (almost transparent) layer to seal in your crumbs-to keep them out of your final coat of icing. This is especially important if you aren't covering with fondant, you don't want to see that in your final smooth coat. Some people skip the crumb coat, I usually do these days.
I really like using a meringue icing like Italian (IMBC) or Swiss (SMBC), they require a bit more work but very fluffy and delicious! I use ganache often as well. There's also American BC that's made with powdered sugar, popular in grocery stores and generally costs less to make.