We have a huge mix of every type imaginable, Brio, IKEA, Hape, Lidl, Wilko, Tesco, World of Imagination, Smyths. Honestly they are all compatible. Some of the really cheap supermarket sets only come with half sized pieces, which are useful to have in a big collection but I wouldn't get a set like that as a main gift.
Personally I'd avoid Brio unless you see a great deal (there usually is for Black Friday on Amazon) only because the other cheaper sets are just as good.
For a just turned 2 year old have a look at the Hape Rainbow puzzle railway and other Hape toddler range. There are all kinds of add one for that, like the xylophone track, jungle train, sensory bug trains etc. Smyth's do a range of wooden toys called Squirrel Play, and they have a nearly identical toddler train set with bead maze and shape sorter track piece for half the price. Lidl usually do a very similar toddler set around this time of year too.
Lidl have some sets in right now, including a jungle set, a dinosaur set or a metro set. Also battery trains. In my experience any set that has sound effect when the train goes over is a huge winner! The battery trains are really popular with my 3 year old but for 2 I'd probably wait for the next birthday for those.