Lots of ways of doing this. I'd first decide if it's something you're happy to do alone, or if you want at least one other person along for company, which would certainly make the journey easier.
Think about what route you want to do, which would then let you split it up into daily sections. For the easier sections, you can manage a higher daily mileage, but a good compromise would be to assume an average of up to 100 miles per day. Use a plotting web site such as bikehike or ridewithgps to work out an optimal route which means you can avoid excessive steep ascents or major A roads, and where your night stops will be. Also make use of Google StreetView for checking out road conditions, width of road etc.
Then decide if you'll use hotels, B&Bs or campsites for the overnight stops, which in turn decides what sort of kit you're going to carry. You should be able to get away with 3 changes of kit in total, washing overnight and then dried on the bike the next day. If you're not camping, then you should be able to get everything into 1 pannier including some non bike clothes. If you're really clever and want to carry minimal items just in a rucksack, you could post kit to the places you're staying, and simply post used kit home each day!