Tax professional (Enrolled Agent) here. IRS laid out their position in Notice 2014-21
https://www.irs.gov/irb/2014-16_IRB#NOT-2014-21. They haven't had much more to say about it since, but they did go after coinbase.com to get information about investors on the grounds that they believe there is a large reporting gap related to crypto transactions. Last I read, a judge ruled partially in IRS's favor, and ordered coinbase to turn over some of the requested info.
Without going into too much boring detail, and not agreeing or disagreeing with specific posts in this thread:
1. Mining is absolutely a business. IRS said as much in Notice 2014-21.
2. Mining revenue is the dollar value of mined bitcoin on the day you received it. Because mining involves frequent small acquisitions, bookkeeping is somewhat burdensome.
3. Once the bitcoin is mined, it's an investment asset in your hands, with a cost basis equal to its dollar value when earned (see #2). Subsequent sale or spending of it triggers capital gain or loss. Again, recordkeeping is somewhat burdensome.
4. Since mining is a business, you can deduct ordinary and necessary business expenses to offset the revenue. Typical expenses would be electricity, equipment depreciation, internet access, rent, etc. Home office expenses would be allowed under the usual rules for that. In your home, a separate ISP account would be needed to take internet expenses, and you need a solid way to prove the actual cost of electricity used in mining. IMO, it's not a good idea to get too aggressive claiming deductions on any home-based business.
5. Choice of entity (sole proprietorship, corporation, S-corp, etc) is a complex topic you should discuss with a competent tax advisor. IMO, for a small home operation, simplest is best. That means sole proprietorship or single-member LLC (which by default is taxed the same as a sole proprietor).
6. If you report losses, you do risk having your mining activity challenged as a hobby. That's another complex issue best discussed with a competent advisor.
7. If you have other business activities, I think it's better to report mining separately (e.g., on its own Sch C).