@devnmark has covered the details very thoroughly and for the most part given all the important information. some input from my side though:
PTDC rama charges a standard rate of 3500 per room and i think that's an unbeatable price point. If you can get a booking there, don't even consider anything else. You wont regret it.
Rama is a hot destination as of late. Get a booking well in advance. I would recommend 2 months prior to your trip because sometimes the entire hotel is booked out by one group so acting early helps.
Some people prefer having their car with them at all times. If you have some mountain driving experience under your belt, you can easily take a swift to Rama and even Bara Pani. The roads are a little rough but a careful driver should not need to undergo repair work upon return.
PTDC staff will book a jeep for you. Back in 2011 they quoted me 4000 PKR for the round trip to Deosai from Rama but i never needed to rent a jeep in that trip or the ones after. If you choose to rent one, you may be able to negotiate 1000-1500 off that price.
I have attached a thread below from my trip back in 2011 on a VW beetle with 4 passengers. While I have visited the area a couple of times since, this is my most comprehensive documentation with details on costs incurred, time taken, places stayed etc. Since then, the roads have only gotten better so if you are willing, considering my car made it, there is no reason your Swift can not make it too.