⚠ Disclaimer !
Due to the big rework on stats, half of this is obsolete (I'll update this as soon as possible). It's still good to go to Undermountain as soon as you can, for companion gear. Priority is to improve items that give percentage bonuses and to get items that have Equip Bonuses that make a difference. Boosting Total Item Level is very important early on, for regular content, but totally useless for scaled content (as long as you can access them).
Refer to the corresponding sections for each part. This is only a rough summary on what you should focus on and in which order.
While leveling, the most important things to get are an augment companion, proper companion gear, and rank 8/9 bonding runestones. Equipment doesn’t matter, just make sure you have a good weapon for your level. Your main hand weapon damage is the most important multiplier for damage and healing. Your active companion and its equipment are the main source of your stats. You will also want a rare (blue) Spider mount for the wanderer’s fortune mount bonus (which will provide you tons of refinement points which you will need later).
Join a high level guild as soon as possible. Not only they will help you, but they will also provide guild boons which are a huge help (8k Power/Defense/ 20% mount speed, or others which may be better for you… and 1500 item level) !
At level 70, you should start the Undermountain campaign. This is where you will level up to 80 and start to get proper gear. It is especially important to farm expeditions there for many good items and most importantly for companion gear (which you can only get there, and is one of the highest source of stats).
Once you are at level 80, your priority is to get the Legion Guard weapons from Avernus Wastes and to upgrade them to legendary. To get them, start the quest "A House in Need" from Sergeant Knox. Then do "A Friend in need" from Alric Vallenhas, then the quest "Tune Up". You won't be able to kill any monster at that point, but the NPCs can kill them for you, and you can sneak around to complete these quests. Once you have your vehicule, you can drive over monsters in the wastes. These monsters occasionnaly drop Treasure Maps. Find the treasures (map from Northside) and hope for good luck. Repeat until you have both weapons. These will help you tremendously !
You will also want to get an epic augment companion (either the Polar Bear Cub if you are focusing on healing, or the Deepcrow Hatchling if you are focusing on being a damage dealer). Any augment companion is good enough as a summoned companion, so a cheap Cat or Watler can do the job to start random epic dungeons.
Now, you can buy your enchantments : rank 9 everywhere is a good start. They are not a priority. So once you have them, forget them. You will upgrade them later, when you have everything else.
You can also buy mounts to be able to use the insignia bonuses and equip and combat powers that work the best for you. Just like enchantments, insignias are one of the last thing you should focus on (though cheaper than enchantments). They are an easy way to balance your stats at higher level. You'll get free epic mounts during events and blue insignias in dungeons. No need to focus too much on them at first.
The next step is to buy rank 13 bonding runestones. These will give you even more of your companion stats, including companion gear and runestones. They are expensive but very worth it ! Do not sell them to buy the next level (unless they are overpriced in the auction house, it’s better to buy rank 13 directly from rank 9, auction house fees can be expensive if you sell and buy all the time). You will upgrade them to rank 15 as soon as you get the materials to do so.
Then, you want to upgrade your active companion to legendary, and to get good passive companions to boost your stats (which you will also upgrade to legendary whenever possible). These are a very big upgrade. As soon as you have your active companion to legendary, rank 15 bonding runestones, and proper companion gear, you can start balancing your stats.
Now, you should be properly equipped. You should be able to start the Avernus campaign. You may need some help at first, but you will be able to get some of the best gear in the game there.
You can also do the Legacy campaigns if you feel like it (you can start them earlier but they are not really a priority). These take a lot of time but Sybella in the Protector’s Enclave will help you with weekly missions (and rewards). Campaigns do not reward much, but each of them will give you boon points, which will make you a bit stronger.
This is when you reach end game. You can now focus on your artifacts and balance your stats with legendary insignias. You can also improve your enchantments, starting with runestones.
The last thing you will have to get, unless you are extremely lucky, is a couple of good Legendary or Mythic mounts for their powers are very helpful in very end game trials.
Once you have everything maxed out, you can eventually improve your mount bolster to 100%, to upgrade your equip and combat power, and your active companion bolster to 15% for the last improvement on your character. Then it’s just about balancing your stats and preparing for the next mod ! And mount collars...