Sounds like a great adventure. Do it and don't be too worried about a lack of experience or expensive kit.

Take a paper map of the South of England for general route planning. You can't carry a full series of OS maps, they are too big and expensive. You could do it on google maps or if you have a GPS.
Your best bet is to use some of the Sustrans routes. These are designed with local knowledge of all the small lanes and trails and the maps are more economical, ie they follow your route.

My basic route planning system is to identify pinch points I have to take, id roads or features I have to avoid, then fill in the details with a local map. I often start the day with only a general direction and no firm route, maybe with the idea of crossing a particular bridge or hitting a small market town for lunch or to visit a tourist site. Sometimes I only start to consider the evening's sleeping arrangements after mid-afternoon.
Cyclist Touring Club (CTC) website is always good for advice as are local tourist info offices and local libraries.

Camping in the UK can be expensive. Commercial sites are usually min £5/day sometimes up to £12 and you have food on top of that. There are websites of small campsites that are usually cheaper. All commercial campsites have showers.
Wildcamping is technically illegal but many people try it. Pick a site that is safe and hidden, arrive late, leave early and be quiet and discreet. You can use bathroom sinks in garages and supermarkets but carry a universal plug.

If you need a good, cheap tent, check out the Gelhert Solo. It is tiny and cheap and should last the journey. Change the steel pegs to aluminium and carry. A big camping store such as Go Outdoors is good value. The Norwich store has almost everything you need in no-name brands.
Cooking will save you money. Avoid the specialist camping dinners except for emergencies. You can use quick cook rice, couscous, noodles and buy tins or fresh veg along the way as you need. You can pick up lightweight cooking kit fairly cheaply or even make your own such as a cat stove. Alcohol stoves are fine for camping and you can pick up methelated spirits anywhere. I use Trangia which is a bit big and heavy by modern standards.

You should be able to manage on 2 rear panniers. A front barbag is good for small bits and as a map holder.
There are plenty of packing lists on the web. Carry enough for a cool, wet evening but be ruthless about excess weight and think dual purpose for your kit. Footwear, tools, cooking stuff, bulk foods all add weight.
Nylon drybags are recommended both for lining cheeper panniers and for racktop carry of sleeping bags. Welded drybags are tougher but more expensive and heavier.
Quick-drying synthetics are your best bet. Polyester T shirts do triple duty for riding, sleeping and everything inbetween. I take 3 pairs of padded shorts because drying can be slow in the UK.
My footwear choice would be a tough running shoe like Silver Shadows and a pair of trekking sandals. Clipless pedals users should opt for a leisure/touring MTB shoe.