You can always wear any clothes you already have (just make sure you have enough to keep you warm and dry), ride any old bike (just make sure it's either in decent enough condition to ride, has enough low gears to get you up any hills/through any exhausted last miles of the day, and that you know how to fix what goes wrong and/or are willing to pay for repairs and replacement parts if needed), and use any old cheap camping gear. A cheap tent will do you, just as long as it'll keep the rain, wind and bugs off you - or go for a hammock setup (www.hammockforums.net has all the info you need to know, also www.tothewoods.net is good). It'll just be heavier and not as durable than if you spent more money. A pad to sleep on will be a few bucks at Walmart, a cheap sleeping bag will again be heavier than necessary but serviceable, and a cheap stove and any pan from home will be enough to cook with.

Weight is the main place you'll be trading off for not spending enough money - also durability, but that's more of a long term concern. With stoves, if you want to save money in the long run, get the MSR Whisperlite Internationale stove. It's like 80 bucks up front (including a fuel bottle if you get it used) but you can fill it with any old gasoline from a gas station, which means it will pay for itself before too long (gas canisters are pretty expensive, comparatively). Plus its super durable and you can take it anywhere in the world. It's what I did and I'd recommend it despite it being inconvenient and that burning gasoline generates a lot of soot.