Matt, glad to see you've thought about this a bit and are taking a responsible attitude. The first thing I'd say is DON'T sneak on to someone's private land and try to do this surreptiously. Not only is it illegal and inconsiderate, it's also unnecessary. You may be surprised to find out (I still am) that, 9 times out of 10, if you ask nicely, landowners are quite happy for you to spend a night or two on their land (as long as you explain what you're doing and how you're going to cope with waste, etc). The alternative is to select a location where wild camping is accepted by convention, or that's so remote, either you won't be spotted or you couldn't possibly do any economic damage.
You need a location that will provide water, fuel and shelter. If you light a fire, not only should you not remove wood, but you shouldn't leave a trace of your fire behind. This restricts you to grassed land (where you can cut out a turf for a fire base, then replace it when you're done) or a beach. Camping in woods is less eco-friendly because your environmental impact is inevitably greater. Having said that, it's useful to be near a wooded area so you can gather fuel and shelter materials.
You mentioned being 'as eco-friendly as poss' and not 'breaking too many rules', but with a little forethought and planning you can do this with no environmental impact and no law-breaking at all. If you don't, then you're exploiting the environment rather than enjoying it, and you need to rethink your approach.
I would try wild camping with a tent and stove first before you go for the full experience, so you can get to grips with issues like locating and carrying water, disposing of your own waste without environmental impact, and so on. This would also help you work out what equipment you need to take with you for your full-on experience.