It seems like what you're looking for is basically a skill list; not too detailed (i.e. not so trivial that it's not worth selecting; see your example of animal handling), but not to general either (i.e. your question about whether ranged is sufficiently distinct from melee combat to a separate item).
So, in that vein I'll just give you what my game uses...
Six Attributes with a dozen abilities and skill in weapons, armor and implements.
- Strength (no abilities; determines load, climb/jump/swim speed and is default for melee attacks*).
- Endurance (Fitness** ability; also determines your deep reserves of stamina used to keep going and fuel powerful spells).
- Reflexes (Acrobatics and Stealth• abilities; default for ranged attacks).
- Wits (Insight••, Medicine and Nature abilities; also used for primal magic).
- Intellect (Arcana, Culture and Engineering• abilities; also used for wizard and gadgeteering magic).
- Presence (Deceit, Intimidate and Persuade abilities; also used for astral magic).
* Fighter classes learn to use light melee weapons using Reflexes and to use bows using Strength (easier to aim when you can actually hold the draw weight for more than a second). Non-warriors are stuck using the defaults
** Fitness is endurance-based because it is mainly used to push past your normal limits of Strength and to resist fatigue, hold your breath and resist environmental extremes.
• Rather than have a specific "thief skill", sleight of hand/picking pockets is a function of stealth while picking locks and disabling traps is a function of Engineering. Climb, Hide/Move Silently and Find Traps have been separated out for awhile.
•• Perception as a skill you can train is silly to me. Your eyes see what they see, your ears hear what they hear. What you're training is your Insight; your ability to recognize what you're sensing as important and recall details of your environment. This is equally good at reading cues from people.
The above array has covered everything I've ever had a playtester attempt. Note that the reason weapons and magic aren't just abilities like Fitness, Arcana or Insight is because I've siloed the combat and non-combat options into classes and backgrounds respectively. Abilities are gained from your background (along with benefits called boons you gain as you level up; this includes non-combat spells), while skill with weapons and attack spells is gained from your class.
Classes are broken down into two groups; Fighters and Spellcasters;
Fighter classes are Brigand, Captain, Defender, Disabler, Mastermind, Sentinel, Sharpshooter, Slayer and Striker. Each class also chooses a combat style (Strong, Swift or Berserker) and combat focus (Daring, Tactical or Wary).
Spellcasting classes are Abjurer, Benedictor, Empowered, Interdictor, Maledictor and Summoner. They also pick a spellcasting path (Astral, Gadeteering, Primal or Wizardry) and each path has sub-subpaths (astral has the faithful, militant and zealous paths; gageteers have the big lug, monkeywrencher, troubleshooter and mad genius; primal has covenant and sorcerous origin with patron spirits that are either potent, swift, clever or insightful; and wizards have lore, social and war variations).
These then combine with a background; Arcanist, Aristocrat, Artisan, Barbarian, Commoner, Entertainer, Military, Outlaw, Religious or Traveler. Each background has a list of six of the abilities associated with it. The character gets two and then any one other ability (on the list or not on the grounds that no background can cover every permutation) and two boons from the background's list (for arcanists these are usually utility magic while an artisan might get "burn the midnight oil" or "rapid jury-rig" (aka McGyver-ing) and a military character might get "battlefield medicine" or "combat engineering").
So that's how I have things divided out in my system.