Please be realistic and practical. There's nothing called "the best training company"—however good it may be. Every company has its own set of strengths and also weaknesses/limitations. What's "good" according to my definitions may not necessarily mean it has to be good for others too, since everyone has his/her own set of parameters when deciding such subjective/intangible issues.
Also, when you haven't mentioned the area/domain in which you want the members to suggest, how can you expect anyone to make suggestions? Training can be imparted in almost every field on the face of the earth—software (again, which one), HR skills (again, which area), soft skills (again, what sort of soft skills), etc.
There's also another aspect you need to look into—you may be keen to tie up with a company, but will they also be keen unless "what you bring to the table" convinces them?
Hope you get the point.
All the best.
Regards, TS