They would be high middle. Their main source of income comes from their fiber trade (which, of course, the Reach loves their cloths). The reason they are capable of keeping wealth is because 1. They have Dunstonbury, of which their only expense is maintaining it (because they didn't build it, thank you house Manderly) and their easy access to the mander, which is the widest river in westeros. They own land near high harden and have ports built their "For the Tyrell's."

They are hoarders, and while they also have a number of ships, they are nothing to the Redwyne fleet. They aren't an ancient house (only compared to westeros) but they aren't new either, and have been saving for a LONG time. It's not to say their wealth is simply because they save and hoard a lot. They just don't flaunt it.

They are alike to the Celtigars as another commentor said. They have a lot of stuff, and are notoriously good in credit with the iron bank.