I think you could do a fair bit for rail in Basingstoke without building a new line. I'd open a new station at Chineham on the Basingstoke-Reading line, and open stations at Basing and Worting on the SWML, and Oakley on the branch to Salisbury, and serve them by (1) extending the London-Basingstoke stoppers to run to Oakley, calling at Hook-Basing-Basingstoke-Worting-Oakley, and also having the London-Salisbury semifast call at Oakley, and anything on the SWML that calls at Micheldever also call at Worting. Won't do much for Brighton Hill area but at least some parts of Basingstoke will then have a convenient commuter service without having to travel into the town centre to get to it.
Chineham is definitely something I'd do. The shopping centre there would be a good reason to open it. However, that's not a particularly controversial/illogical opinion -- there have been plans floating about for a station there for years and with Green Park becoming a reality, Chineham could definitely go ahead.
I stand by my opposition to a line through to Alton though. The answer to transport issues lies in planning more carefully in general, and fundamentally whether rail or road, I don't think it's good to be ploughing up yet more greenfield land. I don't think anyone is going to change my mind -- I love trains and railways and use them a lot, but I'm not persuaded that churning the land back up achieves any more than pursuing greener road transport such as buses running on alternative fuels.
New build housing in Reading, for instance, has been built along the IDR and redevelopment has transformed what used to be a squalid/derelict part of the town centre into something more pleasant to be around. Basingstoke itself got what we call 'Festering Place' (Festival Place, and despite the nickname it is a wonderful place to shop) to contain the shopping centre in one place and has actually been relatively constrained after all the new town build post-war. Sustainable development and transport really does need to stop thinking in terms of 'let's build something new!' and finding more creative ways of using what we have. I wake up to birdsong every morning because the planners of my estate had a creative approach to building houses round a pedestrian walkway/small park rather than just concrete and tarmac roads. I had to get rid of my front garden because as disabled I couldn't look after it satisfactorily and it ran riot during the warm, wet weather over the past couple of years, but I want to try and preserve nature elsewhere.
Sensitive development thinks about how to create a path for humans through the natural world. I don't agree with paving over the countryside with roads either, although some could be better maintained. When I made the original comment in this thread I was cold and tired from a long journey where I'd missed just about every connection I possibly could have missed, but thinking more clearly about it now it just doesn't mesh with contemporary approaches to development.