(2 part post):
Here's a suggestion for you:
Take a train to Doncaster. Find a cheap B&B near to the station. (Doncaster Tourist Information, 01302 734309, should be able to suggest somewhere). Take the 0535 Airport Arrow bus from Doncaster Rail Station to Robin Hood Airport. (Fare �3.50 single, �5.00 return) This arrives at 0600. (If this is too late for check-in, book a taxi instead. It's 7 miles so probably about �15). Take 0645 Thomsonfly flight to Jersey. Arrive 0805.
That 0645 flight goes on Mon, Tues, Thurs & Fri (Not Wed). For the sample dates I've just tried (in May) the flight is FREE (+�18.50 taxes & charges). You could, of course, avoid the B&B charge by trying to sleep overnight in the airport but an easier way might simply be to travel on a Saturday. This is because the Saturday flight goes at 1200. This would allow you leave home early on Saturday morning. The fare (on the sample date I tried in May) is �11.49 (+ �18.50 taxes & charges) but this still works out cheaper than paying for a B&B. (Also, you'll definitely be able to get the bus rather than pay for a taxi). If you travel on a Sunday, the flight goes at 0900 which, because there aren't many early morning rail services on a Sunday, would probably also mean staying in a B&B (or in the airport lounge) overnight.