Crossrail platforms are over 200m long so it's really important to be in the right part of the train if you don't want a long walk when you alight.
So I've been up and down the line to check which is the right part of the train to be in, and I can confirm that generally you want to be at the front or the back of the train, not in the middle.
Let's take it station by station, starting by assuming you're heading to Paddington.
PADDINGTON
2
3
5
7
← Paddington
Paddington has two sets of escalators leading off the platform, both of which head to the same place so it doesn't matter which you take. One set is located between carriages 2 and 3 and the other alongside carriage 7. Alternatively if you're trying to change to the Bakerloo line you want carriage number 5 instead.
Paddington's easy to remember... always sit near the front or the back of the train, unless you want the Bakerloo in which case sit in the middle.
BOND STREET
Davies Street
Abbey Wood →
9
1
1
9
← Paddington
Hanover Square
Bond Street's not open yet, at time of posting, but when it is you need to be either at the front of the train or the back of the train for a fast exit.
TOTTENHAM COURT ROAD
Dean Street
Abbey Wood →
9
1
1
9
← Paddington
Tottenham Court Road has two exits, the new one on Dean Street and the old one where the tube lines are. For the original interchange be at the very front of the train heading east and the very back heading west. For the new exit you want the other end (and also ignore the evil 'Way Out' signs on the platform, just head out direct).
FARRINGDON
Barbican
Abbey Wood →
9
1
1
9
← Paddington
Also simple. The big Farringdon exit is at one end of the train and the lesser Barbican exit is at the other. Getting out in the middle just means a longer walk.
Moorgate
LIVERPOOL STREET
Abbey Wood →
9
2
1
8
← Paddington
For Moorgate and the Northern line be at the back of an eastbound train or the front of a westbound train. For Liverpool Street and the mainline station be at the front of an eastbound train or the back of a westbound train.
WHITECHAPEL
Abbey Wood →
7
3
← Paddington
Whitechapel only has one exit so you want to be in carriage 7 heading east or carriage 3 heading west.
CANARY WHARF
Abbey Wood →
8
2
2
8
← Paddington
For the Jubilee line be near the front of an eastbound train or the back of a westbound train. For almost anything else, including the DLR and the shops, be near the back of an eastbound train or the front of a westbound train.
CUSTOM HOUSE
Abbey Wood →
8
7
2
3
← Paddington
The quickest staircase up to the exit and the DLR is located between carriages 7 and 8 heading east, and between carriages 2 and 3 heading west. If you prefer an escalator, be in carriage 6 (east) or carriage 4 (west) instead.
WOOLWICH
Abbey Wood →
8
2
← Paddington
Very similar to Whitechapel. There's only one exit so be in carriage 8 of an eastbound train or carriage 2 of a westbound train.
ABBEY WOOD
Abbey Wood →
1
To leave the station or change trains aim to be in the front carriage. You can also change trains easily from the centre or the rear thanks to two new footbridges.
And if it helps we can simplify all this further.
Imagine the train divided up into Front (first 3 carriages). Middle (next 3 carriages) and Back (last three carriages).
Here's where you want to be.
EASTBOUND Paddington → Abbey Wood
WESTBOUND Abbey Wood → Paddington
FRONT
Bond St (Hanover Sq)
Tottenham Court Road
Barbican
Liverpool Street
Canary Wharf (Jubilee)
Abbey Wood
Woolwich
Custom House
Canary Wharf
Whitechapel
Moorgate
Farringdon
Tot Ct Rd (Dean Street)
Bond Street
Paddington
MIDDLE
Paddington (Bakerloo)
Paddington (Bakerloo)
BACK
Bond Street
Tot Ct Rd (Dean Street)
Farringdon
Moorgate
Whitechapel
Canary Wharf
Custom House
Woolwich
Canary Wharf (Jubilee)
Liverpool Street
Barbican
Tottenham Court Road
Bond St (Hanover Sq)
Paddington