If your trainer is aware of your skills and you rode with her in the discipline you are continuing then she should know what to look for. If you are still in the just starting out and your budget allows then she should be looking for a schoolmaster.
If you are advancing and are beyond the beginner level with a feel for working with a horse that has the basics but needs work to advance then she could find one started for you to train and learn under a good instructor. Horse may need some training rides but would not be project for the trainer or you could still go with a school master to continue advancing on until you are more comfortable.
As for trainers preferences that depends on the trainer. Around here we have everything from ponies to full drafts or draft crosses to TBs, Paints, QH, Appendix, and WB. What you have is what you ride or you ride the schoolies.
They are a mix of the above as well.
Now if your trainer knowingly arranges a purchase of an absolute greenie that has to trained to your discipline before you start riding then I hope she had your permission beforehand. I also would not recommend the purchase of a more advanced upper competition horse for you to learn on. Your trainer will be riding to keep that horse tuned up costing you $$$.
Some horse people change their horse, they change their tack and discipline, they change their instructor; they never change themselves.
Last edited by QtrBel; 08-12-2020 at 02:59 PM.