Best way to make Pizza dough without owning a kitchen mixer? My last few attempts have ended up lacking in stretchiness...

I've heard of people using a food processor to make pizza dough but I've never tried it.

The recipe I use for pizza dough:
1.5 cups warm water, 1 tbsp *instant yeast, 1 tbsp sugar, 1/2 tbsp salt, 1.5 tbsp of olive oil, 3-4 cups of flour.

Just dump it all into a bowl (start with 3 cups of flour first) and start mixing until it combines, then knead it for like a good 5-10 mins if doing it by hand. It should feel smooth and soft when you're done. If it doesn't, keep kneading it until it does. If it feels too sticky, add a bit more flour and if it's too dry add a bit more oil.

Once your ball is formed, oil a bowl and plop it in there and lightly oil the top. This keeps it from drying out. Cover it with a dish cloth and either put it in your microwave or oven with the light turned on. Don't heat it! Just the light to keep it warm.

After about 20 mins (no longer than an hour) deflate it gently and divide into 2. Should make 2 large pizzas!

*A note about instant yeast: If your yeast doesn't specifically say "instant" go to google to get the conversion for regular yeast and make sure you "proof" it before you use it. With instant yeast you can start mixing it right away and don't have to wait for it to rise first. It's convenient. Just keep an eye out on what the recipes call for.

Another tip with dough, specifically pizza dough, I know a lot of people say to use flour to roll out their dough, etc... but I've found that to cause a lot of problems for me. After your dough has risen, you really shouldn't add more flour to it because you won't be activating the gluten which makes it elastic (kneading process). It works for some people, but I oil my hands and the pan instead and just use that to keep it from sticking everywhere. It's less of a mess and keeps the dough nice and moist.

Never actually kneaded dough to make pizza. Instead I used this SeriousEats guide on no-knead pizza dough and it's worked perfectly I think.
slice.seriouseats.com/archives/2013/01/the-pizza-lab-the-worlds-easiest-pizza-no-knead-no-stretch-pan-pizza.html
Anyone that has done both the standard kneading method and no-knead method care to explain the drawbacks and pluses of each?

I don't understand why people have an aversion to kneading. It isn't hard to do, especially if you're only working with enough dough to make a pizza or two.

This
Buy one at a garage sale for $20

I made this a few times and it works well youtube.com/watch?v=rkI-2zTJWyg . Make sure you really knead it thoroughly or it will rip when you flatten it.

Why are you using 1TBS of yeast and even 1g of sugar, let alone 1 TBS, for approximately 1lb of flour? Don't gnash your teeth and wring your hands about your pizza coming out looking more like shitty bread topped with tomato sauce and cheese, than a pizza.

Without seeing your recipe or method, I can pretty much guarantee you're adding too much flour.

Use whatever recipe you were using, take out about 20% of the flour and set it to the side. Don't knead it in later, don't flour your surface. Just stare at it. See if this helps.

The folks talking about 'no knead' methods are correct, and those who say 'just knead it' are fools. Maybe you have 20 minutes to do nothing but stand in front of a ball of dough, but in the real world most people don't, and folks working in restaurants, pizzarias, and bakeries certainly don't. Yes, powerful stand mixers are another option if you have one, but they're not necessary, and people were making these kinds of doughs long before stand mixers were even a thing.

The trick to working with any kind of high-hydration dough, like a pizza dough, is to start with high gluten flour, mix all the ingredients together, give it a little kneading to ensure complete mixing and get the process started, then put your dough into a refrigerator* for 24-48 hours before you're going to bake it.

That's literally it - dough with yeast working in it will develop all of the available gluten on its own without any human intervention required. All you have to do is plan in advance how much dough you'll need, then top it and bake it.

(*- the dough must be kept in a cool place, otherwise the yeast will go crazy and eat ALL the available sugars and the end product will be overwhelmingly tangy when baked)

No knead all the way
It's the 'proper' technique for pizza anyway and will actually result in way tastier and way better texture than anything you could make by kneading.
Let it ferment for 3 days in 10-15 celsius for best results.

Thanks mate that's some good advice right there.