Where's that tech tree magic?

So I'm fresh off my first extremely embarrassing loss in Endless Space and I need a little guidance so I don't repeat the showing. I mainly researched the exploration and expansion tree and I found myself horribly under-equipped weapons-wise. So after watching ship after ship get shredded under the guns of the enemy, I figured I needed to spend some time on the military tree. That didn't work in time. Which was bad.

SO... how much do I need to divide up my researches to maintain a viable balance? I also noticed that I go some military hardware on the tree I was traveling down, mainly increased ship sizes, but I hadn't grabbed them as I went past. Are those the things meant to keep the tech tree viable?

The magic is in the combition of bigger hulls (bottom tech), higher grade weapons (top tech), bonus volume (right tech), and bigger fleets (left tech). Unless you are playing as a research bonus race such as the Sophants, this can be challenging to have all of this ahead of your opponent factions.

Bonus volume allows small ships to pack more weaponry, making them better at killing everything. Large ships take longer to build, but they can pack in effective defense (against the AI) while still managing a good weapon punch.

To break into Endless Space, I'd recommend playing on a low difficulty level as the Sophants. They research fast, and their ships travel fast. This allows you to explore the tech tree, and use less fleets to attack and defend.

I tend to go for the fleet size (left tree) and ship tonnage (bottom tree) first, bonus ship tonnage (right tree) third and only upgrade the weapons themselves (top tree) when I feel there's a pressing need. I do this mainly because in that order, the incidental upgrades I get benefit the whole empire, (such as unlocking better planetary facilities, colonization tech, and so on), whereas upgrading missiles ... just gives me better missiles.

Plus, I once watched a fleet of destroyers with a single dreadnought flagship tear through a fleet of dreadnoughts and cruisers of equal fleet cap and near-equal weapons tech. It was very scary.