I've been considering going no-till on my garden too. Tilling more than once or twice a year on this red clay we have here will get you BRICK. I have had to add lots and lots of organic matter to my soil to get it loose.
My plan is to establish permanent "beds" and permanent walking paths. Mulch, mulch, manure, compost and more mulch. You just keep adding to it and what is on the bottom gradually breaks down and feeds the soil. You also have to keep something growing on the spot year-round, a ground cover of some sort. Bare soil is a no-no. The sun bakes it and kills off all the good things. A healthy ecosystem of bugs, fungi, microbes, etc. is what you are going for.
Tilling beats them up, kills them and displaces them (the good things.) There is a lot of wisdom in it, certainly, and that is how nature does it, but it's initially more work regarding the removal of weeds. But in the long run you will end up with softer, looser soil and less dispersion of weeds. I have faithfully pulled and removed pig weed from my garden for 6 years now, but every time we till, more come up from the bottom of the soil to sprout again. It's the weed's survival mechanism. No-till will help break that cycle. New weeds brought in by wind or birds (or composted manure) will be easier to pull up and remove before they can go to seed.