£60 won't get a lot and what it will get is going to be broadly the same. You're best off looking at the 'box shifters' for the best deals (occasionally deals elsewhere are worth it, but usually only on the run up to Christmas).
Hattons in Liverpool (
ehattons.com) is pretty good usually and they have a few Train-sets in that price range. Hornby's 'Caledonian Belle' (£48), 'Devon Flyer' (£56) and 'GWR Passenger' (£56 - Due in stock soonish) train sets are fairy basic sets, as is Bachmann's 'Jack the Saddle Tank' set (£54), and have broadly the same contents ('Caledonian Belle' has one less vehicle).
Pushing your budget up a bit is Hornby's 'Codename: Strikeforce' set (£76) which has some army vehicles in it in addition to the railway stuff, Hornby's 'Railroad' Blue Rapier (£76) which contains a three coach (additional coaches are available separately) slightly basic Class 395 train (headlights only) and their premium 'London 2012 trainset' (£80) which is also a 3 coach 395 unit but with more detail and in a fictional Olympic/Paralympic livery. Bachmann nearly matches that with it's 'Class 220 Voyager' set (£83) which has a three car class 220 unit (additional coach should be available separately), and is basically the proper 220 model Bachmann make (head and tail lights, etc), but only three coaches.
Digital trainsets are probably beyond a three year old, but they start upwards of £100.
Normally I'd say that well known auction site is worth a look, but, honestly, if this is for a child I would want to buy new.
I would say that the cheaper models here offer more 'playability' because they are not set train formations, in that respect the Class 395 and Class 220 sets are less good value. That said, the 220 and 395s are, imo, better models and less likely to stall on points.
Whatever you do, don't lay the track directly onto carpet, get a piece of wood or something to put it on.