The tutorial missions give small stacks of some good materials (or maybe I've just been lucky). You might be tempted to hoard those, but I'd heartily suggest using those materials (or anything else you get through events/etc early on) to make good gear right out the gate. Thanks to how the crafting system is designed, hoarding rare materials isn't as useful as it is in some games.
For example, pick up the 1-handed blade recipe as one of your first techs and pump a few chunks of mithril (I got some from the tutorial) into a sword. A mithril sword + any old shield is a pretty solid all-rounder choice, and mithril blades are light. Decent in the front line, and all that shielding can be used from the support line.
Later on, I've found crossbows to be a decent investment. While bows are often so weak as to be dead weight, crossbows aren't much heavier and help flesh out the support line (in combat, ranged attack is used by the support line to buff the attack of a combatant). Can be reasonably cheap, too - iron & string yields 50 weight, 7 ranged attack. Works well buffing a blunt weapon user, as the ranged attack buff becomes blunt damage.
Don't be afraid to use the non-lethal options, and when using non-lethal don't be afraid to use autoresolve (as long as you're not playing iron man, I suppose). The autoresolve is pretty iffy in regular combat, but the lack of wounds/casualties from non-lethal options means you're fine as long as it wins (and it's not too bad about winning).