I think the advice about not worring about breed rather look for what you want in price, age, size and temperment. Find a good horse that is what you are looking for. Low price, 7-10 years old, good build, good temperment GOOD LUCK. You will get all that but the low price. Low price will get you, higher age, less build, or worse temperment. Just remember you get what you pay for.
Pretty much any breed with the proper confo and temperament would be able to do what you ask.
The only problem I think you might run into is the cow work. Any horse can be taught to work a cow, given enough time spent on them, but that takes a lot of work. If you don't buy a horse with previous cow experience, your best bet will be a stock horse with some form of cowhorse breeding in his lines. They will instinctively want to work a cow, even if they don't know exactly where they need to be. They want to be in the right place and you only need to show them.
Where, with a non cowy horse, you have to constantly correct and drill and drill and drill just to get them to stay active in a pen of cattle.