You could easily house six non-breeding birds in an enclosure of this size. Four is a bad number and often leads to fighting, and it is best to do either two or six or more in a cage. Six birds are able to form a pecking order that cannot happen properly with just four. Five would leave one bird without a companion, as birds often pair up. Society finches are the single exception, often bonding into trios.
Firstly I would recommend a lot more perching variety in there. I would try to set up smaller horizontal branches in the front left and right corners and at least one, ideally two different swings from the roof of the cage, perhaps hung from screw-in hooks. The twiggy ones you have are very good, but some less branchy ones may also be appreciated, as would some thin willow twigs or similar that have some bounce to them like a natural tree does.
With many birds of different species in the cage, even without one gender, you do not want the nest baskets, they will still induce territorial aggression. Instead I would attach some silk/plastic leaves and flowers to the branches, for both cover and aesthetic, positioning them higher than surrounding perches so they are not rapidly soiled. This makes the birds feel a lot more comfortable and gives them some privacy in which they will often retreat behind to sleep. Some birds will be uncomfortable sleeping exposed on a branch.
With your cage design and plan for a small flock I would leave the center of the cage mostly open and provide food in a large crock dish on the cage floor. This allows all of the birds to feed at once with room to spare. I'd recommend making a jar bird birdbath [ see here
http://www.finchforum.com/viewtopic.php ... d+bath+jar ] so the birds can bathe as they wish (they should be allowed every day) without making a mess and without soiling their water too much. I have used these before and they are perfect for inside cages like this where you can't hang something on the side and an open dish would make a mess. I think some aspen shaving bedding would look very nice in the aviary and a lot better than newspaper, and that is what I would use, though it is your decision. I think such a nice cage should be set up to be as pretty as possible, though.
Some of the birds you express interest in are a little sensitive. A pair of society finches (two males, I'd recommend) might be a better start, and you can add more exotic birds when you're a bit more comfortable. I would avoid zebras entirely due to their violent nature. Gouldians and silverbills are a bit more delicate than societies, but they're also peaceful when not breeding and would be the birds I'd recommend getting next, as they are hardier than waxbills. Other good birds that are not too hard to care for and not too feisty would be orange-cheeked waxbills, which are among the easiest of the family to please, as well as spice finches, which are very hardy. I would not try cordon bleus, goldbreasts, or strawberries yet.
Overall the care needs of any finches are not too hard. Always access to fresh water and a good quality seed mix. I also provide a good pellet mix. Cuttlebone needs to be available in an accessible place and fresh food should be provided a few days a week at least - broccoli and green leaf vegetables of any type are always favorites, and sweet corn is always well recieved. A little bit of smashed boiled egg (with shell) offered twice a week is a good start, as this is an important protein source. Waxbills also appreciate mealworms and other insects to eat every now and then, making their care a bit more complicated (though they may do fine without these.)
For the more social finches, even if you do not keep more than one of each type, I'd recommend keeping at least two birds of more social species so they have a friend they can relate to. For example, spice finches, societies, and silverbills are close cousins and have similar behavior. A spice and a silverbill are close enough to form a bond whereas a society and a gouldian or a silverbill and a canary are not. A society and a gouldian (or silverbill and canary) will get along as cagemates, but will not become best friends - a gouldian (or canary) is not as social and will not preen and cuddle with a society (or silverbill), which the society (or silverbill) will want to do by its nature. A spice or silverbill, or even a zebra or a waxbill, all cuddly and social birds themselves, would be a better match as a friend for the more social bird. So if you got one silverbill I would not put him with only gouldians, for example. Make sure another more "touchy" bird is also present so he has someone to buddy up with. The Gouldian, however, being less touchy by nature, would be better as the only of its type amongst other species as long as it has some other birds to be near so it feels it has a flock.
The last part is just an obersvation of mine. Gouldians, canaries, other parrot finches are unusual in that they never cuddle or preen like other finches do and so they don't make the best friends for more social birds, even though they may not be aggressive.
.