The route depends on how far you want to run, if you want to get buses, etc. Really, it's just getting the train timetables and matching them all up.
The Hainault Loop: The Central Line runs from Ealing Broadway - Hainualt (via Newbury Park) and West Ruislip - Epping (via Woodford) in regular service. The problem is Hainault to Woodford. You may get a through train, but if you miss a service you will lose 20 minutes waiting for the next one
Mill Hill East: This operates a service from Finchley Central. You may get a through train but you might just miss one. Again, 20 minute delay.
Kensington Olympia: This operates a limited service from Earl's Court, but there are NO through trains. (Cheat: with Kensington Olympia, you may like to get an Overground Train from West Brompton. But you have to either arrive or depart Kensington Olympia by the District line.) Trains are once every 20 minutes.
You are at Edgware, just having cleared that branch of the Northern Line. Your options are returning back to Zone 1 with the train you were just on, wasting over 30 minutes, or get a bus to Stanmore or run to Canons Park, to pick up the Jubilee Line. You will 40 minutes to get to Zone 1, but will have cleared an extra 13 stations. This works as
Edgware - Stanmore/Canons Park
High Barnet - Cockfosters/Oakwood
West Ruislip - Ickenham
Wimbledon - South Wimbledon
Obviously, these work in reverse too.
Coming back from Epping, you have no option but to use the Central Line. Same story with Amersham/Chesham, but with the Metropolitan. So start at Epping and end at Chesham. (Amersham/Chesham takes 2 hours!) Other problems are Heathrow Airport (Heathrow Express from Paddington?) or Richmond (Just have to come back).
So many routes it's hard to list them all. North Ealing - West Acton is the best.
Get a travel card. Only option.
No. You will have to change this on the day. (i.e. There's a signal failure at Croxley, and the route from Moor Park to Watford is suspended. Your options:
1) are to wait at Moor Park, hoping that the service will resume, knowing that every minute you wait exacts a penalty.
2) Abort attempt.
3) Change route (go to Uxbridge first?). Go back hoping the station(s) are open. At least you will have done extra stations.
So changing is the best option.)
Be at Cannon Street before 8pm. Cannon Street closes at 9pm - the train HAS to stop for it to count. So just because you done everything but the District line and are on the last train to Upminster, it won't count. (the last train passes through Cannon Street at around 0047.) Cannon Street is also closed on weekends, meaning that you have to do this on a weekday. Once, Steven Karahan (record holder for only two weeks before being beaten by Geoff Marshall and Neil Blake) went through Cannon Street at 2056. Normally the station is open until 2100. But, due to signal problems earlier that day, Cannon Street closed 5 minutes early, meaning that the time wouldn't count and he aborted the attempt. So be there early.
Don't get the first train! I personally recommend start at Epping at around 0545. This isn't the first train, but it means that you can catch the first Woodford - Hainault service and by 0645, you have knocked off 1 of the three tricky bits. Epping is also remote and it's impossible to get to any other railway (apart from the Epping & Ongar Railay from North Weald to Ongar - just brings you further away) from Epping, giving most tube challengers no option but to sail back down the Central to at least Leytonstone. Starting there removes that difficulty and the time won't start until the doors close at Epping.
Amersham and Chesham are annoying. Very. Ever since the Metropolitan Railway opened in the 1860 from Paddington to Farringdon they extended it through Wembley and Harrow. A branch went to Uxbridge, another to Watford, and another to Chesham. There the line went to Amersham (today's Metropolitan Line). From there the line went through Aylesbury to Quainton Road (now a museum) and split into two branches, one to Brill and one to Verney Junction. From there, the Metropolitan railway planned to continue to Oxford (imagine getting the tube to there!) before it was taken over by London Underground. LU had no interest in going to Oxford, so the line past Amersham was scrapped. The whole Metropolitan journey just going Chesham - Chalfont - Amersham - Moor Park - Watford - North Harrow takes over 2 hours! A massive time sink of 8 stations an hour. At that rate the whole challenge would take 38 hours (if the trains ran 24 hours).
Get a good night's sleep. You will be doing lots of running and spending 18 hours on trains or other public transport - and you thought half an hour to work was bad! Get the nearest hotel to the start station - get a decent one. Don't bring luggage unless you want to carry that around the tube - it will slow you down.
Get a friend to come with you to stop you driving insane - make sure they are a decent runner. Also get more friends to come during the day to get food and drink - unless you can function properly for 18 hours without food - I can't. (YOU DO NOT HAVE TIME TO BUY ANY!) Have some independent person (member of LU staff would be fine) to start a stopwatch, and give that to a friend - do not carry it yourself if you want it to be official. Make that person give it to the last witness to stop it. Do not carry it yourself if you want a record. Do not make a friend stop it - it won't count. You also need photographic evidence you were at a place, a log book giving a route and times, and a witness book with random people signing it.
As I said, you just have to match up all the timetables to get a route.
This falls under Maths, but in a way it also relates to Travel as timetables (essential) come from the TfL website. This will take A LOT of planning. I would start at Epping and end at Chesham. It's up to you though. Print out all the timetables, and try to synchronise it so you are at Finchley Central, Leytonstone and Earl's Court at exactly the right time to get the 1 in 20 minute trains.
The record isn't all about sitting on a train all day. You wil be running a lot, and the route is up to you. People start and end anywhere - Amersham, Chesham, Epping, Upminster, Morden, Heathrow - it varies on the day due to early or late trains, commuter traffic and signal failures. That's why it's such a hard challenge. Jack Welsby done it once and got the record the first time. That's it for him. Geoff Marshall has done it 20 times and only broke it once (Lucky 7). He is still trying.