People often try to avoid spending the money to rent a car here in Iceland. I *strongly* recommend that you rent a car. The country is so sparsely populated that there isn't much bus service to places outside the capital, and and is *no* train service in the entire country. And while Reykjavík is a great, fun city, the country's "natural pearls" are in the countryside. Get a car, drive the Ring Road, and take all of the side trips you have time for - I promise you won't regret it! :)
I don't know anything about Hostelling International.
You have received very good tips earlier, all recommended
Hostelling International Iceland is a very good service, specially if you are on a tight budget. Used a lot by younger tourists so you would have the chance to give and receive Iceland tips in the evening. Staff is usually very helpful with owner often in the reception. They have rigid quality control and usually you get more than you expect.
The roads in Iceland are quite bad so you should rent a jeep. And in Reykjavik you should be really careful because Icelanders drive like maniacs.
It must be enjoyable journey by a private car in Iceland. If you don’t have a private car than you can rent it. It is an easy process to rent it from your nearer. For any kind of help please visit this link. The link is given below.
If it were me, I would rent the car. That way you can stop and go whenever you want. These guided trips are great to get oriented, then go back to what you want to see more of with the car.