I am pretty sure any skills you get from one class will carry over on that character. There may be equipment restrictions like no dual wielding proficiency for Terror Knights but generally the stuff increasing your hit % and damage is good.

You don't want to have too big of a roster as it becomes unwieldy to maintain and level all those different classes. Starting classes like Knight, Wizard, and Cleric remin useful throughout the entirety of the game. How many skill points that character has accumulated and spent is what matters most.

So it's best to stick with what you got and experiment with a few a long the way as you get class marks or recruit characters. Recruiting a character in a class you want is better than changing their class from the menu, since they'll gain some EXP to start with at the end of the battle. So make sure you got a Sybil or Cleric with Recruit when dragoons start showing up. You'll also have opportunities to save a lot of story characters and the ending has a lot of different scenes based on who joined your cause.

A few rules you probably want to know about how EXP is distributed at the end of battle: classes represented by more than one unit in the battle will get more EXP than those with only one. Lower Level classes get more EXP than higher level classes.

You might be having a hard time Jiro since the game is more about passive skills and strategy than it is about balance. You want to have a couple big play-makers stacked with higher level passives and really pay attention to movement and positioning. It can be a little more intense than a lot of other SRPG but that makes it more rewarding.