Travel in group and try to stay in homestays... cook food yoyrself... travel through public transport... and with around 5 6k you can visit anywhere in himachal uttrakhand in car too ....
You can do any job and travel.. well if you are determined try for defense jobs .. in military or anyforce... you can choose mountaneering and traveling as a sport and be in the expedition team
I think you can plan for anywhere in the period Nov. to middle of march. bcz it is best period to go for hangout. since you want visit at this time so you can come to visit Goa, but there is too hot at this time.Plan accordingly