I almost always play The Arbor and it is possible to break off of the reach as such, however it isn't easy. You have to either rush for retinues or focus on upgrading castles to give you more levies. Alternatively you could focus on gaining more and more gold, and rely on mercenaries to fight the Reach when/if it declares on you. The advantage here is that the Reach has to use ships to invade The Arbor and you can effectively hold off a large amount of troops that are coming in at half morale vs your full morale troops. If you have a lot of archers, you can break them quickly and not have to worry about too many losses. In a desperate situation, you can embark your entire army and try to siege Highgarden and hope to capture the Lord Paramount.
If you start at any territory on the main land, you lose the advantage of the sea and the Reach will always curb stomp you. However, if you can endure the Reach as the Arbor, you can fabricate claims on Oldtown, or even marry into it somehow to gain the duchy. The combined strength of Oldtown and the Arbor should be enough to handle main-land conflicts, but an ally would be very beneficial, perhaps Dorne or Westerlands. I've even had Myr or Lys come to my aid before.
As for the Iron Throne, it is possible but it depends on who is ruling. To be able to go toe-to-toe with the Iron Throne you need to basically ONLY hold The Arbor, and possibly Lys and other islands. You just can't beat it in a main-land war. I've only ever been able to rival the Iron Throne after spending decades upgrading The Arbor and taking Lys. You will have to be able to raise 20-40k troops and you will be playing very defensively.
Personally, I don't mind being under the Iron Throne, especially if it keeps me as a Lord Paramount or a Free City.