I knocked down and am rebuilding my 20x24 garage, but want to have more electrical power than the 12/3 that was running out there. My house has an old 60 amp load center that I want to replace soon, along with a bunch of knob and tube wiring.

I was thinking of putting in a 200 amp load center, and pulling new romex through the house one room at a time. However I want to use the garage mainly for a shop. My biggest power hog piece of equipment is a Miller TIG welder that I just got. It will draw 67 amps peak of 240v power. That load combined with air compressors, exhaust fans, lights, etc. leads me to expect at least 100 amp service to the garage. What kind of cable would this require, something like #4 or thicker? Is this feasible through an underground conduit to a panel in the garage from the house? Or would it have to be an overhead feed?

Or would it be best to plan for the garage to have it's own meter and drop from the power company, with 100 or 150 amp service, then work on the house at my leisure. I'd like to get the garage done soon . . .

Not an electrician but did work for the power company for several years.  Are you in the ciy or out in the country?  Do you have your own transformer or do you share with neighbors.  Before you start pulling an additional 100 amps you better check to make sure your transformer can handle the load.

I don't see why there would be a problem running it underground.  The electic company runs major lines underground, so do my parents on their farm.  As for the specifics about the size wire and the best way to hook it up, I can't help you there.

Why not drop the 200+ amp load center at the garage and feed the house from there at a later date.  I have two friends who did it that way and it worked out pretty well for them.

How far apart are your house and garage?

Weigh the cost of X number of feet of #4 copper times 3 (2 hots and a neutral) to the cost of a new load center.  Also if the run is too long you'll have to consider voltage drop.  Some utilities will charge full contruction cost for the second metered point at the same residence also.