Which research should I prioritize for my main troop type?

Troop type is chosen per army (one type, carried by all 3 dragons). Since the per-type Damage/Defense research is targeted, concentrate it on the type you field most:

• Mostly playing Spearmen? → level Spearmen Damage (and Spearmen Defense if you defend). That's exactly Adel's main type.
• Same for Cavalry / Archers / Shieldbearers.

⚠️ Don't spread your research over all 4 types: +0.8%/level diluted across 4 is almost nothing. One type maxed > four half-done.

Alongside that, level the global levers that help all your armies: Relentless Assault, Dragon's Army, Army Expansion. Those don't depend on the type.