Hi. I usually start my roots (rhizomes)indoors on a thick mat of moist paper towels by the sink. I also have a window--no direct sunlight and overhead lights above my sink. I turn the rhizomes over once a day and make sure the paper towels are moist. Barring that, I use a small pot or container of vermiculite, moistened. Lay the rhizome lightly under the surface in indirect light. Only water to keep evenly moist--not sopping wet. Using a plant pot lined with window screen, panty hose, etc. helps excess moisture drain out...yes, no misting with a sprayer for me--I hose them down making a spray using my thumb to deflect water. Both methods take around 3-4 weeks. At any rate, you will begin to see nodes start to green up, then begin to send up a shoot. At that point I pot up the rhizome in a pot that has potting soil mixed with perlite. Perlite offers exceptional drainage. I usually put in a fourth to a third...
As for garlic, again plant as you would a regular bulb-depth. In a pot, drainage, drainage, drainage. Also, graduating the pot size may help. Small bulb, small pot till the bulb gets bigger, bigger pot, etc.
Potatoes shouldn't give you grief about sprouting and there are many examples out there on growing them in pots or pot-like structures. --The issue may be drainage. In the past, I've seen potting soil sold with perlite in it but in recent years, they seem to leave it out. I just buy a separate bag and add my own.-- If for some reason, your potatoes will not sprout, it could be due to it/them being treated with a chemical that prevents sprouting. Did you buy the potatoe(s) from a grocery store? You may want to try washing them, drying and leaving them in the bag they came in in a darkish place. Or, try getting the coveted potato from an organic store. Or...Place cut potato eyes in a worm bin. Worms dislike potatoes and something in the worm castings help plants sprout.
I should have bulleted this but I hope this helps.--There is a lot of misinformation out there about grocery gardens. Here's a pic of my grocery cabbage.
