Bus is one such less costly way to reach Kedarnath. There are buses till Guptkashi from where you could hire a cab or shared local taxi to reach Kedarnath. Total cost comes between 2k to 3K. Another way is from Gaurikhand you could trek the way up, but it’s a 16km trek. To reach Gaurikhand from Dehradun there are direct buses. Total cost comes around to 1.5k to 2.5k. By train till Rishikesh junction you could reach then take a bus or a cab to Kedarnath. Cost comes around to 1.5k to 3K.
For The cheapest Solutions. Get a train from Delhi to Haridwar. Reach Haridwar and take a stare transport bus to sonprayag. From there get a traveller to Gauri Kund And from their trek begins to Temple, roughly around 20-Km. Now for stay options it's betteer to stay in Guotkashi as it has various options.
For Reference : https://traveltonirvana.com/