Swordmen are a solid choice, for the extra point you get an +1 WS, +1I and you can use yur shield in combat so are more ressilient. Halbadiers form a nice detachment just like Free company do. In the end it's what you like more, the St4 of the halbadiers or the extra attacks from the free company.
The battalion is a good start for any empire army.
-State troop are the heart ad soul of an empire army
-Handgunners are nice for some raged damage
-Great swords are just awsome with their stubborn , 4+as and +2 strenght(even if they always hit last)
-Knights arn't this good in the current edition if you ask me but their speed could give you a nice tactical advantage. And let's not forget having an 1+ AS makes you difficult to kill.
When playing empire i advise you to buy at least one Warrior priest. He aids in your magic defence and can boost himself and other charachters. Ow yeah that's right making a unit inbreakble isn't that bad aswell
. Other stuff you might want to get are flagellants as they are unbreakable and have 2 strenght 5 attacks the first turn of combat.