That's a bit more complex (but more logical) than rock-paper-scissor :
Line infantry are the most many of the 3 classes, so they pack the most firepower. Perfect to form the first line of attack. Choose them if you want to play like a tank.
Grenadiers are less many but take the advantage at close range, thanks to their grenades. They are elite trooper so are on par with line infantry (their training making up for their number) in melee. They may play like line infantry but they risk being outnumbered. The best may be waiting for friendly line infantry to occupy enemies, or march behind them as second line, to come close enough to throw grenades. Choose them if you prefer a bit of strategy to come close enough from enemies
Skirmishers are the most mobile, so they are perfect to hit and run or ambush enemies. However, they will really not last long if they are caught in enemy fire, or if enemy attacks them with the bayonet (they have no bayonet)