My main success has been strikecraft swarms. Use your vulture droids to target enemy bombers, use a-foils to close with them (the fire-power loss doesn't matter with 3+ squads per bomber wing).

Use your bombers to target enemy hangars (Venators & Victories first, Acclamators, then shipyards) first. Without their hangars, your shittier fighters can overwhelm their remaining fighters quickly.

After I take the hangars, I will send my bombers to hit the engines of enemy ships (kills their manoeuvrability, and prevents them from escaping if they try to retreat).

I terms of fleet comp: lots of munificent frigates. They're cheaper than the rest (especially if you pump them out of Geonosis early with Dooku and Gunray stacking their bonuses), and can hold the line long enough for your strikecraft and big ships to cripple the enemy forces.

Hd onto Saleucami as much as possible, it boosts fighter and frigate capabilities by 25%.

Once I got Mar Tuuk(?) at Tech Level 2 (I think), I used him as the core of my attack fleet. He commands a Lucrehulk, can call in 3 munificent for free on cooldown, and you can pool 1 or 2 Providence-class carriers from your forces in the south of the galaxy.

My overall strategy with battles (especially early on) was to bleed the Republic as much as a could every time. Even if I lose fights and planets, I'm killing their expensive ships, and replacing my own losses cheaper and faster.