Lovebird and Budgie living together, but not in the same cage?

I'm getting a baby lovebird in a few weeks as well as eventually a baby budgie as my other budgie died.

I'd like to 'raise' them together but I know full well that they can't be kept in the same cage. My question is, can I own both at the same time, raise them 'together' both from babies, or would it be better to go with one or the other? I'd prefer two birds but the love bird is a definite, I've been waiting on the breeder to start breeding them for months and the first of the eggs have just started hatching yesterday and I'm so excited - but I'd also like a budgie, yet I wouldn't want them fighting or anything. If I'm handling one, should I leave the other in their cage or would they be okay out at the same time as long as I supervise? Maybe it'll depend on their personalities.. I don't know. I'm aware they wouldn't usually get along, as is why they'd have separate cages. There's also an adult cocktail in the house that belongs to my sister but they'd be kept separate and wouldn't even know the other exists. Advice please.