What is the best way to remove tiles?

That is an ambitious project. If you remove the grout first the tiles will come up easier but you will probably end up using a hammer and chisel to remove the tiles anyway. I have seen some DIY shows where they have a jack hammer type piece of equipment to aid in tile removal which you could check into renting. In order to get a good laminate job afterward requires a super smooth surface so replacing the old sub-floor is a step in the right direction. Good Luck!

Use a chisel and hammer to remove the tiles. Do not pick up the subflooring as there will be nothing to lay the laminate on.

An alternative, if you like the tile that's there, is to chisel up a few scattered tiles aside from those that are cracked, and lay new tiles down in a scattered pattern so it looks like it was meant to be that way.

I did a lot of tile removal when I gutted the house we now live in and I found the most efficient tool was the Bosch demolition hammer/drill that I bought that has what the call an SDS-max bit connection, and I bought a 1" wide chisel bit. These demolition hammer drills have a mode that vibrate axially (they also have mode to drill) and the chisel bit literally explodes the tile. Sometimes the entire tile pops up as one piece but more often than not it busts it into many pieces with some section tenaciously holding onto the floor, but it won't stand up to the chisel butting its head against the tile at 3000 times a minute. Lighter versions of these hammer drills like I have go for about $200 or more industrial versions can be rented by the day. Wear safety glasses, ear plugs and dust mask because it does produce shrapnel and a lot of dust.