To my knowledge, the order in which you train/do rides doesn't matter, unless you're aiming for an easy BLUP, in which case it might benefit you to do one or the other first (you can look up BLUP guides for particular breeds as it varies depending on their strengths).
The benefits of rides do stop, but only when you've maxed out all the skill points you can get from them, which (as far as I know) doesn't change depending on when you do it - it's just a set amount based on genetics.
They stop gaining skills on missions based on age (once they hit 25) but that's separate to rides.

the best order to do things depends on breed. there's guides in the "howrse-breeding" forum

Hiram....I did see the guides in the breeding forum. I was a little confused on those as well. I'm using this one as an example since I have Criollo's.

Does this mean in do forest rides until they can no longer do forest rides and then dressage, jumping, trot training one after the other until they are finished. Do i do trail class competitions while i'm doing the mountain rides or do i show those until i get 20 wins and then do mountain rides?

Cutting (e.g. Argentinean Criollo, Arabian, Vanner, Morgan, Canadian Horse)

* Forest rides
* Dressage training
* Jumping training
* Trot training
* Trail class competitions
* Mountain rides
* Reining competitions
* Gallop training
* Speed training
* Cutting competitions
* Stamina training

I believe it means do them in the order given, not simultaneously. The reason for this is because if the skills that the rides gives you contain the difficulty-determining skill for the competition, it will increase the difficulty level of the competitions your horse is able to enter. Sorry I do not know the western ones off the top of my head but using classical as an example: if the ride gives an increase in gallop skills, completing the rides increases the difficulty level gallop race the horse can enter, making getting wins harder.

The advise in the Howrse-Breeding forum is excellent. Tried and tested over many years.

I would advise do them in the order given until you begin to understand the patterns and how they affect competitions. The 20 comps are the hardest part of blupping a horse and until they are blupped you will not get the best foals when breeding. Also you cannot enter the
best competitions until you have 20 wins.

Overall the trick is to avoid training the main skill needed for the competition you wish to use but making the other 2 skills needed as high as possible so that you enter the easiest competitions with overall better skills than the other horses entered. Done right it works like a dream.

Thank you for the explanations!