Hammerheads are indeed excellent destroyers, and if you're doing the beginner tutorial you'll get a free one pretty quickly (albeit with a d-mod or two). I usually run them with a mixture of railguns, arbalest cannons, and heavy mortars in the forward-facing guns. All of those share a pretty good range that the AI can handle well without being too aggressive.
Overall, I find that the utility of frigates drops off as fleet size progresses. Once each side has more than 1 cruiser, then using carrier-deployed fighters and bombers is more reliable for the longer time of battles. I try to make sure I'm not using ships with a burn speed of less than 8, which ultimately works out to a mix of cruisers and destroyers, supplemented by a few destroyers for pursuit work (wolves, lashers with Safety Overrides, other fast frigates). The Brawler's combination of long 'Peak Performance Time' and strong reactor mean that they're still useful in larger battles, though.
Among the vanilla options, I tend to prefer the easier maintenance profiles of mid- and low-tech ships to high-tech ones. E.g. the Medusa may be powerful, but requires a fair bit of maintenance and can't handle successive deployments too well. Condors make great, relatively cheap carriers from early game to late game. Lashers with Safety Overrides are superb, but only for short decisive engagements. Despite being high-tech, an Apogee is an excellent flagship for an exploration fleet that can still handle itself in battle.
If I were to recommend some faction mods that I don't consider too unbalanced, I'd say Shadowyards Reconstruction Authority, Underworld (adds a bunch more pirate-type ships), the Junk Pirates suite (some of the ships/weapons are probably underpowered, but they're generally neat), and maybe Diable Avionics (might be a tad overpowered).
Probably just as important as fleet choice, though, is skill choice. I usually get a fair number of the industry and tech skills before doing any combat ones at all, which I'm sure changes how I approach things - the skill that halves the negatives of d-mods, for example, makes a huge difference to me.