I would just take some quality garden soil and mix it with compost, or worm compost (is pretty nice). It makes your soil more alive and nourishing, before you fertilize it with fertilizer. 
The best time to plant the garlic cloves may be in fall, they like a cold period to grow better. 
But you could just plant them now and wait a year or probably more. I did that last year, and after a full year of being in the ground, the garlic *almost* started to look like a full bulb, but it would still need some more time. I separated the cloves and planted them again, the other two I will leave them until fall😁 

 If I start growing them now, it shouldn't have a large impact on flavor though, right? 

 I don’t think so👀 it just could take longer 
I have noticed, garlic = patience :D