I wasn’t a fan of minis until 4e came along. The introduction of very tactical combat made the conversion easy. I enjoy the different perspective that a large mini represents on the battlefield, how lines of sight might be affected and how the battle in general unfolds. Of course it has also led to several members of the Dungeon’s Master team to develop rather large collections of minis. Which is all to my benefit as a player and DM.
One of the questions I’m constantly debating is whether to use a mini that matches the monster they player’s are fighting. Now let me clear up that last statement. If the players are fighting a dragon, a beholder or a giant I use the appropriate mini. The dragon might not be the right colour, thought that’s usually not a problem, but the mini at least represents the monster.
Where I’m less specific is with humanoid combatants. My half-orc’s might look like humans, and my minotaurs might look like elves. As long as I have a mini on the table I’m usually satisfied.