TexasMomof5
Hello from Canada, and welcome to the Forum.
I'm glad you've decided to live your dream and get some birds

.
First of all, making a cabinet aviary, is not an easy job, but there are several members who have done just that. Not sure how good of a carpenter you are, I know I'm not, lol.
You would definitely have to do your research on safe paints, lighting, safe door openings, screening, air circulation, how to attach perches, removable bottom tray for cleaning, etc.
Regarding your bird choices...
Now Finches and Canaries, are similar in many ways.
They need flying room from side to side for exercise. A finch without the room to fly (exercise) is not a happy bird, and will tend to become obese and may develope health issues.
Usually the absolute bare minimum length is considered to be 30 inches from side to side, with wider being better, and with the height not being quite as important .
Finches and Canaries, are not hands on birds. They do not want to be held or petted or played with. They don't do tricks or learn to talk, but they are amazing to watch.
Male Canaries sing, females do not. A Canary on it's own is alright, as they tend to be solitary birds. In most cases, males prefer to be alone, and will not get along with other males, some will even fight.
Finches on the other hand, are social creatures, and do not do well on their own. There are many different species to choose from, and that is another story for another post.
Now Lovebirds and Budgies, are hookbills, and if handraised from a very young age, can become quite tame and attached to their owners.
Although they enjoy flying, they can also enjoy climbing and can get quite a bit of their exercise doing just that. They also love toys.
Finches and Canary, can be housed together in most situations.
However Finches/Canaries and Hookbills should never be housed together.
Budgies and Lovebirds, should not be housed together either, and some Lovebirds can become very aggressive and nippy .
Regarding live plants....
There are some safe plants, and some unsafe plants (there is a list in the Finch information center).
That said, most live plants will simply get pooped on and eaten by the residents and will have to be replaced on a regular basis.
Finches however do enjoy artificial greenery to play with and hide in.
For Hookbills, it's not recommended as much, as they may eat them.
Hope this was helpful.