How to seal where the wall meets the floor?
There are several ways the air can reach the gap between the floor and wall.  Your best solution would be to find the entry point and seal it there.  Unfortunately, that's almost impossible so your next best answer is to seal the gap between the wall and floor.

Your first answer, caulking above &amp; below the baseboard, is the least obtrusive but would be the least permanent.  As the wall and floor flex with changes in temperature, humidity, and load, the 2 seals could break loose.  The seal against the floor is also likely to be knocked loose with regular sweeping and foot traffic.  Although better than no seal, it's not my preferred approach.

I did similar to your second answer in the laundry room of my own 1929 home.  I removed the baseboard &amp; trim, stuffed any gaps over 1/8" (2-3mm) with foam, then caulked over the foam and reinstalled the trim &amp; baseboard.  It's amazing how much air leaks through such a small gap!  The water lines to my washer froze several times before I sealed the gap; the space hasn't dropped below 50F since I sealed it.

If you remove the hardwood to replace it, remove the trim as well and use the opportunity to seal any gaps where the wall meets the floor.  Walk around the floor inch by inch and screw down (not nail!) anyplace that moves or squeaks.  A simple web search will find more about eliminating floor squeaks.  Also look into a roll underlayment to go between the subfloor and new, floating, laminate.  This would isolate the laminate from the subfloor to eliminate another source of squeaks and cover gaps in the subfloor, reducing drafts from below.