There are two ways you can reach Manali from chennai at a less cost. Travel by bus to Delhi or take a train to Delhi. From Delhi there are buses to Manali. My advice would be stay in Delhi for a day, because journey from chennai to Delhi is for long hours.
The cheapest way to visit manali from chennai is plan a train to new to new delhi & from there bus to manali but it nearly takes 50 hrs of journey
the fastest journey to manali from chennai is make a bus plan from chennai to bangalore and then flight to Chandigarh airport there cab to manali it reduces nearly 24 hrs of your journey
MAKE THE JOURNEY SIMPLE BROTHER NOT COMPLOCATED
You didn't mention ur budget, any how by train from Chennai u can travel upto chandigarh then u could pick transport vehicle to reach manali, it takes nearly 50hrs, after u reaching manali, many home stays are there, it is better to stay in a budget, according your plan that how many days u are willing to stay, by that ur expinditure will be fix, rent a bike at manali and cover local places it is better then taking four wheeler, food, accommodation, traveling all u can complete ur trip in 10 days if by train, by air ur can complete with in 5 days, by train means ur budget 15k, by flite means ur budget 25 to 30k.