Start with an SO frigate or cheapo destroyer. Use point defense weapons to max out damage-per-flux early on, they're good sources of kinetic pressure. Safety Overrides turn all bad ships into good ones.
Ideal ships: SO + hardened subsystem + speed hullmod + annihilator + machine guns Lasher, restored Luddic Path Lasher with more of the same, broken down SO Enforcer with lots of Heavy Machine Guns, etc.
Eventually find Something Cool. This may be a black market elite frigate/destroyer purchase, some modded exploration or event content, or a lucky kill/faction salvage. Sometimes it's a rare weapon that can define a ship. Proceed to build fleet, skills, and officers around cool flagship.
Ideal ships: plasma cannon SO Sunder, any of the modded elite destroyers/frigates, Tempest, Harbringer, maybe a really early Doom or SO Eagle, etc. My favorite modded ships at this point tend to have mobility abilities first, cool built-ins or ship systems second. I spend a lot of time drawing attention with minimal fighter cover and picking off stragglers.
Endgame is determined more by fleet composition, which is mostly a matter of faction commission or colony blueprints. At that point the flagship is complementing whatever the rest of the fleet lacks. I kind of prefer long range artillery boats with burn drive and auxiliary thrusters - dual Gauss Legion with shield bypass and escort frigates, dual Devastator Onslaught with mauler/HVD mediums, etc.
Ideal ships if modded: BRDY Karkinos, that underworld pirate flagship with the turret and burn drive, other artillery capitals. If the mid-game coolship was something ridiculously fun like a Sylphon Rakia (SO on it is amazing fun) or other phase cruiser/super-destroyer it might be my preferred endgame ship. Some of the smaller player-bait ships start to get tedious when you're grinding through large fleets, but phase ships with interesting mechanics never get dull.