I'm going to Iceland in the second half of June and plan on exploring the west (all the way to Snaefellsnes) and the Westfjords. I'm also planning on taking road 35, which is a seasonal road that links the north to the Geysir/Gullfoss area. Would a 4WD Subaru Forrester be able to handle it or would I need a higher vehicle? Also can anyone recommend a good car rental company with affordable prices?

The Forester is a good choice for these roads. Any 4WD is good for these roads, Octavia, any Subaru, Ford escape, Vitara, Jimmy and many more. There are no river crossings, only rough dirt roads.
B-)

Check out http://nordiccarrental.is/
I rented a small car from them last week and they even delivered the car right in front of the hotel.

We just came back from Iceland. We used Geysir Car Rental. Their price was very reasonable. We were very happy with the their service. Due to the airport closure, we were rerouted to Akureyri. Icelandair provided a bus to bring all the passengers to Reykjavik bus station. When we called them from the bus terminal in Reykjavik, Geysir Car Rental was really sympathetic to our trouble. They delivered the car to our hotel free of charge. Normally, it would cost you 30 EUR. The staffs were very friendly. We returned the car to their office in the airport. It was pretty easy.