Hi and welcome!!
So first off is you don’t have to get two birds. If you have the bandwidth you can have one birds you just need to be able to spend the hours with it. If you don’t think you can then I’d get a second. Personally, we have a flock that we maintain just for that reason (among other reasons).
The size of the cage correlates with the size of the bird. There are a lot of different types of birds that fall under the parakeet umbrella other than Budgies. However, the idea still stands: you want to get them the biggest cage you can afford. For Budgies they typically do better in cages with more width than height. Bar spacing is a big thing. I believe for Budgies it’s .5” to keep them from getting their heads stuck in the bars (birds are inquisitive, I’ve had bar stuck heads before). If you get two you need even more space, I have a flight cage for mine and I believe it’s the f5050 from prevue and I like it a lot. I’ll link it here as well.
I used to have dogs when I fostered a sun conure. What I would do with my dogs is put them in a separate room or their kennels and let the bird out throughout the day so they’d spend a max of about 2hrs at a time in their own space and then I’d let them back out after putting the conure away. I’d do that at least 2x a day and I kept him on a 12hr sleep schedule as well.
Here is the link: flight cage
If I missed any of your questions please point it out! I’m glad to answer any other questions you may have as well! 😊