1) Weapon counts:
Frigates: 4-6 small weapons or 3-4 small weapons and one medium weapon, etc. If a hangar bay exists, 1-3 weapons. The more weapons, the less defense or higher the DP as a counter-balance. A built in wing is generally smaller and replaces slower than standard module wings, and either costs more DP or takes the place of a weapon or two.
Destroyers: Same number of small weapons but also typically 3-4 medium weapons. Slightly greater defenses and lower combat speed than frigates. Less maneuverability. Slightly higher DP. Destroyer carriers get 2-3 hangar bays (Epiphany now has 3 for the next update). Same number of small weapons but 0-1 medium weapons. The presence of a medium weapon should remove a hangar bay or have very high DP.
Cruisers: 8-12 small weapons and 4-6 medium weapons and 0-2 large weapons. Same stat differences that differentiate frigates from destroyers but by a larger margin comparatively. Carrier cruisers usually have 4-6 hangar bays and only 6-10 small weapons and ~2-3 medium weapons. Combat cruiser still have 2-4 bays, but can't use them as efficiently as carriers (will discuss details further down)
Capitals: 15-30 small weapons -- 8-12 medium -- 3-6 large (variance depends on DP/defense/role). Much higher defensive stats for capitals and low speed. Like cruisers, non-carrier capitals have 2-4 inefficient hangar bays while carrier capitals have as many as 10 efficient hangar bays. 10 is the max because with the hullmod bringing the total to 12 that is the most the UI can reasonably handle in the refit screen.
Weapon layout guidelines: Weapon arcs and position are such that at least 2 small weapons can be used for PD at most directions for a frigate or destroyer and 3-4 can be used for a cruiser. Capitals have the most overlapping arcs, but keep in mind that you can't overlap too many arcs for both aesthetic reasons and because that is oftentimes wasted ordinance when considering lots of small targets. At least 3 large weapons and 4 medium weapons should generally be able to focus fire on one target in the case of capitals.
Sprite size guidelines: Each weapon size is one size smaller relative to vanilla. So vanilla medium is AO large, vanilla small is AO medium, etc. From there, sprite size generally scales with OP cost or possibly the range of the weapon. Fighters are a lot smaller than vanilla, but typically have similar wing sizes. They replace slower and have less standard range than vanilla wings since carriers will buff these values with hullmods.
Weapon flux cost guidelines: Short range, low armor penetration and fast firing weapons don't usually cost flux. These are considered assault weapons. PD weapons also don't cost flux. Heavy assault weapons, such as the Railgun or Dual Railgun, fire with 0.2 - 0.4 flux efficiency considering they are longer range than the standard assault weapon. Strike weapons deal a lot of damage very quickly, but fire with 0.4 - 0.8 efficiency or have a lot lower sustained dps. The higher the armor penetration for an assault weapon, the lower range or DPS it probably needs to have. Fire support (or very long ranged) weapons have greater than 1.0 firing efficiency and lower sustained dps in most cases. Missiles are different. Many strike missiles don't cost flux but have very low sustained dps and can be heavily mitigated by PD (see Atropos) and long range missiles are also heavily mitigated by PD but have better efficiency to fire (~0.5 - 0.

compared to non-missile fire support weapons.
Designation details: (these are done using built-in hullmods -- more of these will be added in the next update)
Frigates: +100% damage to strike craft -- +50% damage to missiles -- maintains 0-flux speed boost until 35% of max flux not considering skills.
Destroyers: +50% damage to strike craft -- +50% damage to missiles -- maintains 0-flux speed boost until 20% of max flux not considering skills.
Cruisers: Either -- (+45% additional non-PD weapon range -- +30% additional PD weapon range -- OR -- +20% additional weapon range) -- maintains 0-flux speed boost until 7% of max flux not considering skills -- has hangar bays unless a phase ship -- OP discounts to interceptors and fighters depending upon tech level/manufacturer.
Capitals: Either -- (+45% additional non-PD weapon range -- +30% additional PD weapon range -- OR -- +30% additional weapon range) -- maintains 0-flux speed boost until 7% of max flux not considering skills -- half the 0-flux speed boost -- has hangar bays unless a phase ship -- OP discounts to interceptors and fighters depending upon tech level/manufacturer.
Carriers (any size): Same designation benefits as warships but also -- half the 0-flux speed boost unless a capital which already has that -- 50% replacement rate bonus -- 100% range bonus for effective wing range -- OP discounts to weapons depending upon tech level/manufacturer.
Phew! That's a start anyway! Obviously these are just guidelines that I go by, and exceptions of all kinds exist in order to create unique ships. At the end of the day, playtesting is important both 1v1 and fleet simulations. I hope this helps give an idea of how to approach a rebalanced faction mod or creation of additional custom ones.