Good advice from these guys. I just wanted to add a couple of things. When you pull out all of the core plugs to flush the block, you may also want to remove the drain petcock on the left side so that you can get as much out as possible. You'll probably gat a lot of crap out of the water jacket. That seems to be normal.
When installing the new plugs I'd use some type of sealant around the outer edge. I use Permatex #9 Tack and Seal. #2 Permatex (the brown snotty stuff) would also work well. I'd stay away from RTV silicone, It may work OK, I just don't like it for that application. (that's just my opinion) Carefully tap the pluggs into the hole, with the domed side facing out, until they seat against the ridge at the back of the hole. To set the plugs I've used a couple of methods depending on how accessable they are. If you try to smack them directly with a hammer it's easy to miss the middle and they won't set properly. I will either set the ball side of a ball-peen hammer against the center of the plug, then hit the hammer with another hammer. Or I've also used a brass drift or punch with a very blunt end, set against the center of the plug and smack it with a hammer. The idea here is to dimple the center of the plug which will try to flatten it out and make it fit tightly into the block.
Good luck, sounds like you're on the right track.
Merle