Hello. The Alexander and Barney are both great cages. You don't need a different cage for them as pups, they can go straight into the Barney or Alexander. Of the two I would say the Alexander maybe, as the overhead shelves make it feel a bit more enclosed underneath for a shy hamster, plus it comes with a good house (the long one), two play houses and you only really need a wheel and some toys.
Usually you leave them alone to settle in for the first 2 or 3 days while they work out where everything is, they scent mark to find their way round and make it their territory and they build their nest.
After that you can talk to them through the bars, feed them treats through the bars and gradually start taming them.
The main thing is they have a nice big dark house to nest in which helps them feel secure and the long house in the base of the Alexander is good for that.
The other thing is a really good depth of substrate - it helps cushion any falls and helps them have normal hamstery behaviour like digging, burrowing and pushing it into heaps
It can actually work out cheaper the more substrate you put in because then you mostly only need to spot clean and only do a "big clean" every 2 to 3 months. Plus they will use a litter tray if you provide one in the place they've chosen as a pee corner.
The Barney would be fine as well, and it also has a good house. It's a little bit more open at one end and people end up adding things usually, (eg another shelf or similar) to give a bit more cover.
But really either cage is great as long as you put loads of substrate in and give them loads of nesting material (torn up plain white toilet paper in strips).