Hey Abhijit.. Rajasthan is very vast so it's very difficult to complete in one go. you need at 15 days to complete whole Rajasthan. I would recommend if you are traveling for the 1st time & solo, you should visit Jaipur, Jaisalmer, udaipur and jodhpur. it will take 8 days minimum to complete these 4 cities. Rajasthan has lot more to discover. problem about Rajasthan is that one city is far from the another city due to that it takes lot of time.
Best time to travel is October and November. February and March. December and January will be very cold.