Open every cache you find

A constant supply of training gear allows you to open caches from the very start of the game, completely risk free. Every Abandoned Cache can be opened using Training Gear as an alternative to Stone. The cost of using Training gear is also significantly cheaper than Stone or Marrow, and will not impact your starting Brick production which is very important on higher difficulties.

Abandoned Caches, especially the large variety, can hold cornerstones to boost your settlement's economy. I have personally received Grain +2 from a cache in my recent Prestige 5 run, which completely snowballed my food production to crazy numbers.

So being able to open EVERY cache for free is insanely good for your early game.

As a cherry on top there are also several Dangerous Glade events with an "Arrest" or "Purge" option, that can be solved using Training Gear.

Trade it away

If you're not using the gear you can trade it away. Having a constant supply of 0.21 x 3 = 0.63 amber per minute (in value) flowing into your stockpile will give you a lot of bartering options. Sell your training gear in either trade routes or directly to a trader for a quick influx of money to spend on anything you need. Buy perks or blueprints, or even trade it for building supplies or complex food.

Don't forget Training Gear can also be used in Packs of Luxury goods. So if you have the appropriate manufacturing building like a Leatherworks then it can be converted to an even more lucrative item for orders or selling.

Stockpile it for Service later

Finally... if you're not opening caches, solving glade events, or trading it away; then stockpiling it for a service building is a very good choice too. Training gear is used to fulfill Brawling in:

• 🏚 The Clan Hall
  
• 🕵️‍♂️ The Explorer's Lodge
  
• 🍵 The Tea Doctor

It is not uncommon to have 100+ Training gear stockpiled in late game to immediately boost your settlement when you finish building one of the aforementioned service buildings.

On higher difficulties it is essential to have a functioning service since the additional storm effects can rapidly harm your population, and some negative perks can also be completely prevented with a service building (similar to the need for Housing and Complex food). So having a service building with preloaded training gear can give you a breathing window of 10-20 minutes, for free!

Should you rush up the tech tree for it?

Yes.

Training Gear Delivery Line is so ridiculously overpowered, that I do believe it worth your resources rushing Vanguard Spire to Level 8 and as many points into Pioneer's Gate as possible. The benefits you receive from Training Gear early will snowball every settlement into a win without fail.