I just removed the paneling in my den. When I started with the base boards and noticed that when when my tile was installed they were installed with the base boards in place. Before I could remove the base boards I had to actually break the grout around them so I could get the boards out. Now that that is done I now have a 3/4 inch gap between the wall and the tile and that is only one side of the room. The other side will have about an inch and a half gap. How should I address this. I was thinking of getting some grout to match and filling this gap in. Not sure if that is the best solution.
You have a 3/4" gap and a 1 1/2" gap, and clearly the larger gap is too wide to be covered by a baseboard alone.
What I might try to do is see if you can get a standard baseboard against the wall which will give you about 3/4", then I would put quarter round right after that against the baseboard.
The 1.5" gap will be hidden, but you might need to cut a 3/4" wide strip of wood so the quarter round has something to sit on. It should be roughly the same height of the tile so the edge of the quarter round will be just covering the edge of the tile. If there any more gaps at this point I would probably get some white paintable caulk and go around the base of the quarter round.
I like this approach because I think a little quarter round around the baseboards of your room can be quite aesthetically pleasing and make a simple boring looking baseboard look even nicer.