Okay, for a class list go
here. You can have any class on this list (even classes marked "enemy only") except for Dark Druid, Arch/Uber Sage, Magic Seal, Bramimond, Fire Dragon, Civilian, Prince, and either Transporter. Those classes break and/or are broken. (That is to say, they either break the game or break the game balance.

)
Clerics, Troubadours, Lords (Lyn) and Blade Lords are specifically female. Mercenaries, Heroes and every other Lord class are specifically male.
To see the battle animations for all classes, go
here, nicely sorted for your convenience.
The first list determines what weapons you can use. If you voluntarily take a class with worse weapon selection or worse movement speed (Armor Knight as opposed to General, for instance) I'll buff you to compensate, but only to a degree. Unpromoted classes will recieve stat buffs to bring them up with promoted classes, so you don't need to worry about that.
If you need more detailed information about each class,
Fire Emblem Wiki is your friend. Just remember, this hack is from a base of FE7/Rekka No Ken/Blazing Sword, so if you're looking for class pages try to find the right one.
How weapons compare to each other: Lances, Anima magic and Bows are middle-of-the-road. Axes and Dark magic have lower hit and higher damage. Swords and Light magic have higher hit and lower damage. Staves are your only reliable source of healing, and also have some hella nice status inflicts, but aren't offensive in the slightest.
Basically, your class will determine your usable weapons, animations and movement speed. Stats are up to you.