There is no one race that's good for all. Gargoyle is uniformly bad for it.
A. For Lumberjacking, you probably want an elf. You get more colored wood (NOT a higher chance, but just more swings) and more of the side items used by Alchemy and other skills.
B. For gathering leather, human is an air-tight lock for best. Higher carrying capacity (1/6 higher than other races to keep from being overweight), and the human +10% bonus to harvested leather stacks with (and is applied before) the +10% bonus for using a Harvester's Blade (from the old turkey events, or from the Huntmaster Challenge outside Skara, where you get 1 reward for each animal each month that you bring in the high weight for). There's no elf bonus for leather gathering, and the lower carry capacity is a negative.
Example: Regular Dragon giving Barbed Leather
Elf/Gargoyle: 20 Barbed leather (40 in Fel)
Human: 22 Barbed leather (45 in Fel)
Elf/Garg using Harvester's Tool: 22 Barbed leather (44 in Fel)
Human using Harvester's Tool: 25 Barbed leather (49 in Fel)
C. For mining, it's a toss-up between Human and Elf.
Human has the higher weight before being overloaded. Humans also have an extra ore drop about every 5-10 digs.
Elf gets more digs, and has a fractional bonus to color amounts (1.2 x the existing percentage of colored ore for that resource square). Devs 11 years ago called that a "20% bonus" for the Elf (but mistakenly thought all squares had identical 40% chance per swing of colored, instead of being random from square to square, ranging from about 10% to 75-80%). In reality, it means that a spot that would give colored ore 10% to a human would give 12% to an elf, while a 75% spot for a human would be about 90% colored for an Elf.
As a result, a Human can haul around more ingots/tools (Fire Beetles are your friend) and stay out longer, while the Elf will get more ore (but have to either use a lot more Bag of Sending charges or run back to drop off ore a lot more often). Whichever is better, is up to the play style of the player. My personal opinion is that the multiple trips and lower overweight cap makes an Elf at a disadvantage if they are in a potential combat area like Fel, mining in a monster spawn area, or using Gargoyle Pickaxes - but slightly better for mining in Trammel/Ter Mur quiet areas (and only a lunatic mines out in the boonies away from the Royal City in Ter Mur, or in Tokuno outside Makoto-Jima). As I personally mine 99% of the time in Ilshenar with Garg Pickaxes trying to bring up paragon ore elementals, I go human. YMMV.