The problems you have with ship combat is one that many starting players have. Yet, there are many players who can take any ship and turn it into a solid combat ship with just a few tweaks. Here are the basics,
1. Always set weapons power to the maximum of 100.
2. Have 2 copies of Tactical Team I. For 15 seconds after activation, this ability automatically transfers shields to the facings that are taking damage. This one ability easily extends your survivability in combat. Cycling the 2 copies of TT allows you to have this ability constantly active.
3. Settle on using only one single energy weapon type for your ship, either all phasers, all disruptors, all antiproton, all polaron, all plasma or all tetryon. Never ever equip weapons of different energy types as that will reduce your weapon's damage. In general for starfleet characters, phasers are an excellent choice.
4. Now that you have settled on your energy type, make sure every tactical console is enhancing that energy type. So for example if you are using phasers, your tactical consoles should be filled with phaser relay consoles, Doing this will significantly increase your ship's damage.
4. Now it boils down to using those weapons effectively. Every weapon type (beam arrays, dual beam banks, cannons, dual heavy cannons, torpedos, turrets) have different firing arcs. Learn to position and face your ship so that all (or most) of your ship's weapons, both fore and aft, are firing. This gives you maximum firepower needed to bring down foes quickly.
5. Generally if you are using an escort, equip dual heavy cannons and a single torpedo as your fore weapons, and turrets as your aft weapons. Point the ship at your target and fire all weapons.
6. If you are using slow turning a cruiser or science vessel, it is best to equip only beam weapons in every weapon slot (no torpedoes). Let your ship's left or right side face the target and fire all weapons.
Again these are just the basics, but I guarantee you will see significant improvement to your starship combat if you follow these steps. Who knows, perhaps ship combat will become fun for you after this.