For me, it varies with the character I am fighting, as well as the stage. Usually, I will (try) to throw away all the old ones, and get a fresh one in my hand. Then, I jump off the stage, and at the peak of the jump (with back to center of stage) pull another banana out. This has the banana land close to the edge of stage. There are several advantages and disadvantages to this:
The good:
1) You will usually be safe from opponent hitting you, since your so far from them.
2) They pay attention to either the banana or you, but both can hurt them.
3) If they get rid of the 2nd banana, you still have the other to aid w/ recovery + have a banana out.
4) It stalls their invincibility time.
5) If they shield the 2nd banana it will bounce up, and by the time it falls they're invincibility should be gone. Not only is this a good time marker for you to get back and attack, but it also puts a banana right next to them.
The bad:
1) They can catch the banana and throw it off stage or at you. Not really bad, just makes you seem like you wasted your time making the banana.
2) They can keep the banana and actually use it. Generally its not too bad since you can throw the banana at them before you grab edge, and can usually get rid of it/get it back. Typically what I see is, they throw it down, up, or hang onto it. If they throw it up, it's an easy catch. Just make sure you've tossed yours already. If down, again just air dodge on it and quick throw. If they hang onto it, who knows. Usually I just Edge->Fastfall->Jump->Fair.
3) The opponent can disregard both, and just go for you. Typically at an angle that you can't throw a banana at them. What I do here is press z to drop banana, then b-air to try and hit opponent and catch banana. (Unless its a character with a fast/long rane aerial, then I dodge)