If you're in the Uk, Fitch is great - I use that (paper bedding, recycled food grade paper). It's sold in bulk. Some people like Kaytee clean and cosy. In the US I think you can get Oxbow paper bedding still. Or the cheapest in bulk is Boxo from Walmart I believe. Or if you have a shredding machine, you could make your own paper bedding by shredding kitchen rolls - not sure how long that takes or how expensive it works out.
But yes, for nesting, torn up strips of plain white toilet paper go down well.
Which country are you in, for recommendations for paper bedding? His cuddly house is also very sweet, but if that is in his cage/enclosure, it would be best to remove it, as hamsters can chew fabric and pull out the stuffing, and there's a risk they can pouch/swallow some and get a blockage, which can be life threatening, or cotton threads from stitching get wrapped round their teeth or legs. They are nice for out of cage time, where you can supervise/keep an eye on it. It may be he isn't chewing it, but it's best to be on the safe side, as that could change.
Ness