I bought three of the Oster on sale 10 years ago. One for me, one for child and one for niece. They have all held up. The combs have each lost tooth or two and two brushes survived a dog chewing. They aren't pretty but still useable. Handy to have matching. Helped keep things from disappearing. I got few plastic sweat scrapers to go with. They sort of it in the carrier. The bags have been washed and dried several times over the years. I can't complain and they worked well for toting to lessons. Niece still uses hers. I have bought some specific brushes from Haas and another company plus pick up things to try when I think I might have a use so I also have a couple of plastic totes that are full. Starting out I don't think you would go wrong with the Oster set.
Some horse people change their horse, they change their tack and discipline, they change their instructor; they never change themselves.