The best next upgrade fixes the problem you already have. Expand the stable or fields if you need space, prioritize the arena if training is holding you back, and wait on specialist facilities until you have a staffing or breeding plan.
Expand when you have a use for more space
If a full yard prevents you from taking a boarder or keeping a horse you want, look at stable and field upgrades first. If you have empty spaces already, spend elsewhere until you have a concrete reason to expand.
Train for the competition you want to enter
If space is sufficient but your horse is stuck at its current training options, examine the arena upgrades. The official game description links advanced buildings to new training courses, staff applications, and a breeding lab. Use the option that helps with your next goal.
Leave specialized investments until you need them
A breeding facility makes more sense once you know which horses you plan to pair and where the foals will go. Staff capacity helps when you already have more care or training than you can handle. Keep operating money aside when you price out either improvement.
FAQ
Does the stable always come first?
Expand it first when capacity is your real obstacle. If you have room but lack training options, the arena may be more useful.
When is the breeding station worth prioritizing?
Move it up your list when breeding is a goal and your yard can support the foals.
What if I can barely afford an upgrade?
Wait until you can buy it and still cover your existing horses’ care.