You are an Indian national and have been issued a Business Visitor visa to the UK. The Business Visitor visa programme was created in 2008 following a consultation by the Home Office and there is a backgrounder at ILPA Info Sheet
Following this consultation, the rules were amended and Business Visitors are covered in Paragraphs 46G through 46L, see Visitors to the UK These are the rules under which your visa was granted. To make his decision, your Entry Clearance Officer used the guidance at Business Visitors
You would like your wife to accompany you and need to know which class of visa she should apply for.
Your wife should apply as a GENERAL VISITOR. She can use the new site at Visa4UK
She can use the VFS and also use the premium service if she qualifies. She can add your information in the remarks section to explain the rationale for her visit.
She does not qualify for FAMILY VISITOR because she needs a UK-based family member to sponsor her, and you do not qualify as a sponsor in that capacity (British citizen, permanent resident, etc). See Family Visitors
For completeness' sake, The only concession made for family members of business visitors is in the case of 'Academic Visitors'. The concession, stated in Paragraph 42 of the rules, is that the family member can ask for the same amount of leave as the primary, up to 12 months. And even in this case, the family member must apply as a GENERAL VISITOR.
For your last question, your original application indicated you would be travelling alone, but now you want to travel with someone. It's a normal change of circumstances and you can put an explanation in with your wife's application.
For your question in the comments, you are allowed to act as a tourist during your visit and to stay for a reasonable amount of time within the leave you have been granted. These things should be incidental to your trip and as long as they are incidental, you will have no problems. To play it strictly by the book, you can declare your touring itinerary to the IO during your landing interview.
You didn't say when your wife will make her application, and you have also indicated that personal experience is welcome. From that viewpoint, the Home Office has just concluded an 'invitation only' consultation and is planning to change the visitor rules sometime before Parliament sits in 2015. This will be the first major overhaul of the visitor rules since 2008. There are links to the consultation and to the draft rules, but they are currently embargoed and behind a paywall. I will post a link here once the embargo is lifted. Personally, there are no planned changes, however, that will enable your wife to accompany you as anything other than as a GENERAL VISITOR.