My son is 15 months old, too, and I can tell you how we handle this. When I first give him food, I only give him literally 2 or 3 bites of food. That way, if he's in a throwing mood, I'm not cleaning up a ton of food. If he does eat up right away, I give him a little more food, but I never give him a lot at one time. He sits right next to me in his high chair, and I refill his bowl as needed.
If he throws his food or starts playing with it, he gets one verbal warning, and only one warning. "Stop playing with your food, or I will take your bowl away and you are done." Then we actually follow through. If he throws his bowl on the floor, it stays there. If he is playing with his food, we take it away from him and then he sits there until we are done eating. My son gets 3 meals and 3 snacks each day, we are never more than 2 hours away from food, so I don't feel like I am taking food from him.
This was effective for us, and we don't have too much problems with food anymore. He caught on quickly that we mean business.
IME, if kids are really hungry, they eat the food, they don't sit and play with it. You've noted yourself that this behavior incresase when it's something she doesn't like or she's starting to get full. If she's not going to eat it, why not take it away instead of having to clean it up? Also, throwing things (cup, plate, silverware) on the floor and then you picking them up repeatedly becomes a game to them--don't play it.
Same deal with a sippy cup, wave it around or throw it and you get one warning, and then you are done. My son has gotten to the point that he will drink what he wants and then just hand the cup to my husband or I--he is "over" the thrill of throwing it.
We heap on the praise when he eats and drinks well. "What a big boy you are--look at how nice you are eating." He gets a big grin.
One last thought--I've seen people put 2 or 3 different bowls in front of a toddler, a sippy cup, and some silverware. IMHO, this is just too much temptation and too much to play with at this age. Keep it down to 1 bowl or plate at a time, and try handing her the sippy cup only when she needs it. One piece of silverware (if she's using it) is sufficient. Good luck.