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I do this journey a lot.

The connection between the Central and Bakerloo lines at Oxford Circus is very easy, which might be why TfL suggest that route. Position yourself at the front of the Central line train, step off at Oxford Circus, turn left as you step off, 1 minute fast-ish walk to the Bakerloo line platform (keeping left at the split then right at the T-junction) with a few steps (one flight but potentially awkward if you have large or heavy luggage). It does work, though it's not my preference on this route. Deep-level tube lines generally have a high frequency service so you won't be waiting too long. If you have time, position yourself mid-train on the Bakerloo train for access to the escalator at Paddington.

I normally take the H&C/Circle and connect to the HEx, as others have suggested. It's a more comfortable journey - bigger cars and air-con. Position either approximately one car forward or rearward of mid-train on the H&C/Circle for best positioning for the stairs at Paddington.

A modification to the above that I frequently use if an H&C/Circle train is not the first train at Liverpool Street, is to take the Metropolitan line train (shared platform) as far as Great Portland Street - step off and then step on the first H&C/Circle train that comes (it's usually next, but verify). Most people seem to only take the Metropolitan line if that is the one they want - as a result, they are often less crowded than H&C/Circle. These lines share a route as far as Baker Street, but only share the same platforms as far as Great Portland Street where you can simply step off and step back on - enough people get off that getting on the H&C/Circle is not difficult. If you go to Baker Street you will have to cross the station to change platforms as the lines diverge just before the station throat.

Timing, whatever the timetables say, is generally an hour from Liverpool Street to the T5 HEx platform. On the HEx position in the second carriage from the front (or alternatively, the forward carriage of the rear unit on a double-unit train, or Business-First carriage of the front unit) for swift access to the lifts at T5.

If you just miss a HEx, as I seem to on a regular basis, add another 15-20 mins - although they leave every 15 mins, in practice the train is removed from the departure boards a minute or two before it actually leaves, so you can be tricked into thinking the train has already left. The smart traveller checks the HEx departures on his/her smartphone whilst the H&C/Circle is stopped at Edgeware Road: Live Departure Boards - National Rail Enquiries to save time at Paddington.

I now realise that I have an OCD with journey optimisation.