I've been making homemade pizza for about 4 years now and have got a good hand-tossed recipe down. Here's a few key points I've discovered (through a whole ton of trial and error):
1. Water temperature should be around 105 degrees. Way my mom always told me to find this temperature was to not make it so hot that you can't stick your finger in, but hot enough that you don't want to leave it in there for very long. Or use a thermometer
2. Mix your sugar into the water and then the yeast and let it sit for 10 minutes before you add it to the dry ingredients. This will activate the yeast and make the dough rise much more.
3. When letting the dough rise, I put it in a bowl covered with a damp dishtowel to keep it moist as it expands. I turn on my oven for about a minute so it gets slightly warm, and then I put the covered bowl with the dough in there to rise for about an hour. I then punch it down and let it rise for another 30 minutes. For this 30 minutes you can optionally put it in the fridge - the cool dough will be easier to work with when you stretch/toss it.
4. Cook the pizza in a HOT oven! I cook at 500 degrees. If you cook at lower temperatures you will get a very evenly cooked pizza that comes out more like bread. The hot temperature will cook the outside much quicker creating a slightly crispy crust with that great chewy inside.
5. Even at 500 degrees which is significantly less than a pizzeria's oven, I found that the toppings were cooking much quicker than the dough. To get around this, I recommend a pizza stone for your oven. Let the stone heat up for 15 minutes to get it hot. Then, put in JUST the dough without any toppings for 5 minutes. This pre-cook will make the dough much firmer and will give it the head start needed. Take it out of the oven, add your toppings, and slide it back in for 5-8 more minutes (you'll also find it's MUCH easier sliding a pizza onto a pizza stone when the dough is precooked and firmer than if you have it loaded up with toppings).
6. I highly recommend making your own sauce from canned crushed tomatoes - I started doing this and it makes all the difference compared to canned pizza sauces. Use a can of crushed tomatoes, and I like to add fresh garlic, oregano, basil, and crushed red pepper for a bit of spice. You won't go back to pre-made sauces if you do it this way.
Again, some of these tips are specially hand-tossed related, so I can't help you on some of the specifics with a deep-dish pizza. Let me know if you have any questions, I'd be glad to share my discoveries.