For A Small Bird (parakeet, parrotlet, lovebird, cockatiel) I would say a good minimum size would be 24" by 18"
by 30", you might think that's huge if you've never owned a bird before, but you'll soon see that it would actually be
a fairly small cage.
Remember that when you get a bird, the cage is the most important purchase, since it will more than likely spend the majority
of it's life inside of it. So it's very important to buy the biggest cage you can afford.
Birds like to climb, so horizontal bars are a plus, but I don't think they are necessary. My birds get around just fine
with their vertical bars.
Those tiny cages that look like houses are cute, but impossible to clean, and are way too small for ANY size bird to live
Make sure you get a cage with a pull-out drawer. It makes it 10x easier to clean!