Your choice of element only really matters if you want to employ a Witch later on. If you make sure that everyone (or most everyone) on your team is of a particular element, you can spam the "battlefield chants" (any of the Goddess' names) to turn the entire battlefield to favor the chosen element. Of course this means that the enemy units of that element will be stronger too, so be sure you can eliminate them ASAP. (Wind seems to be the best choice here, since you can also use the valkyrie spell Storm to change the battlefield, plus valks fight better in storms) You'll also find elemental weapons later on, they basically make your melee/ranged attacks magical attacks of the appropriate element.
Spells are heavily dependent on the battlefield's dominant element. They'll have a larger AOE, do more damage... etc. They also do more damage vs units of the opposite element (duh). Like baby arm said, have your casters use spells of their own elements and try to stand on a spot that has a bonus to that element (not always doable, depends on map).
Early on, you'll want everyone to have a ranged weapon. My usual setup at the beginning of the game is Short Sword / Short Bow / Leather Armor / Healing Herb.. you don't have clerics yet, so having accessible healing is important. After you turn some of your females into Archers and Clerics, you can start switching your meleers (who should be berzerkers or knights, and valkyries eventually) to heavier weapons.
Some classes favor a particular weapon, this becomes apparent from a different animation they have with said weapon type. Knights and dragoons like swords (kek), zerkers like axes, archers like bows (give your crossbows to other units), dragon and beast tamers like whips, valkyries and angel knights like spears.
If someone with a bow has the higher ground, they can usually hit targets farther than their maximum range, generally one extra tile for one level of elevation. Be careful when you're facing archers high above you; I find that flying units and spells work best against them.
Spears can be devastating against tight groups of enemies. Take this for example:
(X)(A)(B) where X and B are armed with a spear.
If unit X attacks unit B, unit A gets hit as well and unit B will counterattack first, hitting unit A again. If unit B has a whip, he'll counterattack and ONLY hit unit A, making this tactic nasty against bosses like Ozma.
Training is a pain, yes. In my current game I haven't had a single training session yet, but that's because I was extremely cautious in all battles and knew exactly what to avoid.
What I prefer actually is levelling up characters in random encounters (to raise their morale). Just bring 7-8 solid characters into the encounter along with 2-3 newbies and have the newbies stay back and throw stones at the high-level characters' backs. They'll usually hit and get good xp. If you're feeling gutsy, you can get them to finish off the wounded enemies for crazy amounts of xp, as well. In general, try to let your less developed characters get killing blows. Don't go overboard and have one person deathblow every enemy on the map, or you'll get an MVP award (extra level) that's usually more bother than it's worth. The enemies scale to your highest level character, so if you have a level 20 and a bunch of 18s.. yeah.
EPSXE works, it's how I played it. You can cheese with save states if you want, I usually save right before questions just so I find out what my character will actually say/do if I choose one of the options. Cheap, but like baby arm said, it's very hard to infer just what the choices mean. There's an excellent reference site at
http://luct.tacticsogre.com -- but it seems to be down at the moment (it was up yesterday, fwiw)
Edit: Another good tactic is to have your heavily armored tank characters shield slam the enemy -- attack with your shield, it'll do almost no damage, but if your weight is greater than the enemy's, you'll knock them back a square. This can be very useful on some maps. For lighter armored meleers, use gauntlets instead of shields (lighter and some special bonuses, but no shield slam ability.. then again, those units don't have high weight anyway).
-- Z.