The best time to visit Rishikesh for River Rafting is from late September - October to mid-November, and then the best time to visit Rishikesh is from early March - April to the first week of May. In July there is a festival in Rishikesh called Savan where thousands of people flock to Rishikesh. Else you can visit at any time of the year.
The best way to travel from Delhi to Rishikesh is by bus or train.
The bus will charge you Rs. 275-300 (the cheapest) from ISBT Kashmiri Gate or you can go by train which will take you in the cheapest way but takes a longer time. The Unreserved ticket cost you Rs. 55 only.
Travelling with your friends will cost you cheaper as local autos and Rickshaws charge you 10-20 Rupees per person. Don't be fool by the auto Drivers. Else you can walk on foot as the distance between tourist spots are from 3-6km max. Travelling on foot will give the best experience ever. Travelling on foot, roaming around there and Singing along with your friends will give the best experience.
Food per day per person will cost you Rs 200-300. Travelling around will cost you Rs. 50-100 per day.
Staying at a homestay will be fun but little bit costly. You can also live in a guest house which will cost you 500-800 per room, In which you can share your bed with 2 more friends. You can also easily Bargain there.
Before leaving set a plan where you want to visit in Rishikesh. Use google maps to get an idea of places nearby.