Take the sucker out. When u buy head of garlic, they should be firm and whole. Store in a cool dry place, not in sealed plastic bag. I'm always tempted to buy the ginormous bag of garlic from costco, but I steer clear, since that's way too much garlic for our small family to use . Unless u have a vampire problem, then go crazy.

take out the sprout it is bitter.

When you cut up that little green sprout, it immediately starts a chemical reaction which causes the garlic to smell a bit off ,.. and the smell grows the longer it is allowed to sit like that. When I was at the Culinary Institute of America the chefs suggested removing before chopping. In day to day, home use, I generally leave it in (unless I am prepping the garlic a little ahead and don't want it to smell off).

In my early years I had many chefs tell me not to use it. Never have and probably never will. It means it gone in metamorphesis so to speak. Its ready to sprout and grow. If you have a garden put them in some sandy soil or a pot with well draining soil and in 9 months you will have grown your own garlic.

That little green "germ" is really bitter, so yes take that out. Garlic, I think, is best left out in the whole bulb. Don't refrigerate it unless it's already peeled. You can confit it ala Keller too. It's labor intensive to remove the germ, or you can just buy more bulbs.