Depends on your preferences. the forts are somewhat similar. if you visit a few, you don't need to visit the rest. I have visited the Amer fort and it was impressive. and you know rajasthan is full of history and majestic things. for different experiences, you can put chokhi dhani (Jaipur) in your itinerary. do visit Jaisalmer and experience the desert safari. rajasthan is nothing without it. also put Mount Abu in your itinerary which is the only hill station in rajasthan. and for the budget, it depends on the time when you plan to visit. in the off season, like October (is the best time according to me) the prices are far less. do you the local conveyances which will bring down your budget further. also if you are interested in something mystery and all, you can also visit kuldhara (can google it) (bhangarh is also famous for such things). enjoy.
I'd you want to experience Rajasthan, trust me it will take time. 7-10 days I would say. Do keep Jaipur, Pushkar, Udaipur, Mount Abu, Ranthambore and the desert safari of Jaisalmer in your itinerary.