How should we setup Settlers of Catan for three players?
There are some good suggestions all over the internet for making a three-player board more competetive in the early game. They all boil down to either removing hexes, or replacing them with desert pieces.

The amount of hexes you replace/remove depends on preference, but I'd recommend either removing three or five total hexes. When removing five, just remove one of each resource type. When removing three, remove one wood, grain and lumber (since brick and ore have one less hex to start with).


When removing three hexes, take one of each number token 3 and 11 and remove them from the game. Then take one of each number token 4 and 10, choose one at random and remove it from the game.
When removing five hexes, take one of each number token 3-4-10-11 and remove them from the game. Then take one of each number token 5 and 9, pick one at random and remove it from the game.


Substituting hexes with deserts means there's still plenty of room for long roads and it puts some distance between viable resources. Also, it allows you to maintain the regular board size. Removing hexes altogether can lead to challenging board shapes, but if you remove exactly five hexes you can still create a hexagonal board:

  X X
 X X X
X X X X
 X X X
  X X


The best way to get a hexagon with 3 hexes removed is if you make it asymmetrical across one diagonal:

  X X X
 X X X X
X X X X X
 X X X X


A third option found online is increasing the VP requirement. This doesn't match your criteria since you're looking to increase tension in the early game (instead you'll find yourself using more of the board late game) but it's still worth mentioning.