1 Join the CTC in the UK, lots of information available on their web site and you get good discounts from various stores.
2 Get a decent lightweight tent, Check out Cotswold Outdoor, reckon to pay about £200 for a decent one, camping is a lot cheaper but it's a good idea to treat yourself to a motel every now and again, costs will depend on where you are, some areas are cheaper than others, Motel 6 is pretty good.
3 Wait until September/October for the sales to buy bike and cycling clothing. Have a look at Wiggle and Chain Reaction websites for kit.
4 In my experience cycle touring is pretty safe, I've never felt insecure at any time. Have a look at the companions wanted board if you feel you might like company
5 If buying a bike in the USA, I'd recommend the Surly Long Haul Trucker
6 I find a couple of cycling tops, a couple of technical Ts and comfortable pair of shorts with a padded liner. I prefer baggies as they have pockets but a lof of people prefer lycra. I'd recommend a set of Gore Bikewear pac lite waterproofs and gloves. Helmet, of course, and also a cycling cap.
Lots more advice on other sites, don't get too hung up on the kit, just go and have fun