May to Aug is the summer time , if you want to exp less crowd and winter go on during September as it will be bearable. depending on your trek pass and days price will vary, starting from 15000 to 30000/- per person
September is the best month to travel to Leh as most of the roads will be in good condition and the entire region reflects green and orange colour. The high altitude lakes will be in aqua blue colour and weather will be pleasant through out the day and colder at night. Budget for the trip depends upon your mode of transport and choice of stay. With shared cabs and hostel/guesthouse stay a Leh to Leh trip of 8 to 10 days can be completed with 15k which includes food, accommodation and transport.
June to August mid is the best time to go. Also in terms of the budget u need to be a bit specific what kinda trip u going whether a bike trip or you would be landing in Leh and travelling by car there.