OK - I can add a personal response here. Basically, I've lost 3 stone this year - not as much as some but I've hit my weight target of being sub-11 stone rather than a tubby 14 stone. I'm also planning Coast-to-Coast (March/April 2012) and LeJog, but it's likely to be August 2012/May 2013.
The bike - any bike can do it, but a road/tourer will be easier. The budget is basically what you can afford, although £500-1000 gets you a decent bike. It's better if your work has a Cycle to Work scheme. Size-wise it depends on height; I'm 5'9" so fit a 54cm (and 56cm just) - check with your LBS (local bike shop).
I've got a Ridgeback Platinum tourer and have put over 2500 miles on it since April - it'll do my Coast-to-Coast next spring plus the LeJog trip and others. I've signed up for next year's Etape Pennines, so it'll be doing that too! Whilst it retailed at £1000 I paid £870 from
Evans by using a discount voucher and cashback website. I've bought a cheap bike off
eBay for the winter as well, which should save wear and tear on the Ridgeback.
Clothing; since you're about to lose weight, I'd go for the cheaper end. Simply put, you'll wear them a few times and find out they're too big (hopefully). I've gone through 4 sizes; XL down to S in clothing since April
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. If you've got a significant other, warn them a load of parcels will arrive
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. Having lost 3 stone, I need an entire new wardrobe too, after my trousers fell down in a work meeting
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eBay's proved great; cycle shirts, padded shorts (the bum's not got the extra padding it had!), helmet, gloves, leg and arm warmers and jackets. All I did was do a search for the item at the size I was and bid on the cheapest ones. Once I'd shrunk they went back on eBay, usually covering the cost I paid. The only difference was the helmet; here I went for the strongest/lightest/best fit I could in white and dayglo green for visibility (a Uvex FP1) and price wasn't an issue.
I've moved onto a pair of Pearl Izumi shorts plus shirts from Sugoi, Kathmandu and Nalini ones. You'll find people put on unworn/hardly worn ones because they're 'last year's design'. If you're losing weight, they're a great choice. Either that or I'm a cheapskate
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What else have I done? I've got a spreadsheet, which maps mileage (plus weekly total), route and weight. Weight was graphed weekly until I hit the target,
which helped with motivation. Don't expect to lose weight immediately - at first it was static for about a month. My weekly mileage is still graphed and I've set a minimum target of 100 miles/week. Also, I'm totalling the amount saved on commuting (£10/day for petrol and parking), having saved over £400 so far.