Ok, so, the basics:
Ships have slots: high, medium, low, and (some have) drone bay.
The high slots are typically for weapons, or mining lasers, or tractor beams, cloaking devices, etc.
The medium slots are typically for shield modules, afterburner / propulsion modules, and various electronic warfare jamming devices.
The low slots are for armor modules, reactor controls and auxiliary power, co-processors, cargo expanders, or weapon stabilizers for extra dps.
The high slots are further divided into Turret slots (for guns) and Launcher slots (for missiles), forcing you to use the weapons that the ship is designed to work with.
Ships also have a power grid and a CPU stat, that will limit the size of the guns and armor and shields that you can put into the ship. Frigates and destroyers typically use “small” weapons and modules, cruisers and battlecruisers typically use “medium” stuff, and battleships use “large” stuff.
Now, if you want to do the Military missions, you need a combat ship, with weapons and defenses. You have two options:
Use the starter corvette, because it’s free. To get one, when you’re in station, right click your mining ship and “leave ship”, this will save the mining ship to that station, and eject your pod, so you can fly around in the pod. Undock from the station in your pod and fly to another station in a nearby solar system; the moment you dock they’ll feel sorry for you that you’re in a pod, and give you a free corvette ship, with one gatling rail weapon and one civilian mining laser. Right-click this ship and make it active, so your pod enters it, then from the left toolbar click your Assets app, and find where your mining ship is, in the list of assets. Right-click that station and “set destination”, which will plot a course with the autopilot. Then undock in your corvette, and fly over and dock at the station where your mining ship is.
Buy a combat frigate; these typically cost 400-600k ISK. Open the market and use the lists on the left side to find Ships, Frigates, Gallente, then look through; the Incursus frigate uses guns, and the Tristan frigate uses drones. Sort the market interface by price, and then in the top half (sellers) try to find a decent price that’s near you (the number of jumps from where you are is listed in the first column on the left). After you buy it, you will need to exit your mining ship and fly the pod to where your combat ship is, to go get it.
But this just gives you the ship, now you need to fit it with weapons and defenses. Here’s a tutorial for fitting ships in general.
For your combat ship, you want some weapons, some defenses, and an afterburner for speed.
For weapons, Gallente ships use “hybrid” weapons, these are weapons that shoot ammo, but use energy instead of gunpowder to propel the ammo. Hybrid weapons (like all weapons) come in two varieties: long range (rail guns), and short range (blasters), and the ammo is called “hybrid charges”. For frigate sized hybrid weapons, you have the following options:
75mm (civilian) Gatling - this weapon is given during the tutorial and it’s very weak, but doesn’t use ammo.
Light Electron Blaster
Light Ion Blaster
Light Neutron Blaster - short range weapons (less than 1km), best used with Antimatter Charge S ammo, or if that’s too expensive, Plutonium Charge S, or Uranium Charge S.
125mm Railgun I
150mm Railgun I - long range weapons (10-20km), best used with the longer range ammo (Lead Charge S, Tungsten Charge S, Iron Charge S)
I’d say try buying 2 or 3 Light Ion Blasters with 3000 rounds of Plutonium or Uranium, for fitting in your Corvette or Incursus in the high slots.
After the weapons, you need to worry about speed - speed is defense for frigates, so find a 1mn Afterburner and buy it to install in a medium slot. This afterburner will let you get close to use your blasters, or maintain distance if you decide to go with long range rail guns.
After the speed, you need to worry about defenses. Gallente ships are usually fitted with armor defenses, and for frigates, not much is needed: Small Armor Repairer, and maybe a Damage Control.
These are the basics, and now you have some free slots. The Military missions will give you some webifiers and jammers to use in the medium slots in certain missions, and otherwise if you just need to shoot the enemy, you can put a Cap Recharger in the medium slots to give you more juice so you can keep that armor repairer going for the longer fights. And for the low slots, a Magnetic Field Stabilizer will improve the damage that your blasters or rail guns do.
Now, you have two extra tools to help you set up your ships:
The Fittings screen has a button on the left side for “Ghost Fitting”, which means you can play pretend and see what you can fit on a ship without having to buy anything. Play with that, get a good fitting going for whatever ship you want to use, then save that fitting or write it down and buy those exact guns / modules from the market.
The market is also an encyclopedia of all the items in the game; you don’t have to buy things, you can just find stuff on the market and right-click it and “show info”, to see what it does, what skills are required, and what “variations” it has. There are different sources of gear; some gear and weapons are made by players, others are drops from NPC pirates. All of the equivalents of a gun, for example, are listed in its “variations” tab, and you can right-click each variation and “find on the market”, to see what it costs. Often you’ll find better damage, pirate drop guns, for cheaper than basic player-manufactured versions.