I agree with Crystal in that you should get a large enough cage that you can afford. I don't know the dimensions of Lulu's cage, but she's in a mansion
Make sure that the bar spacing is no wider than 1/2 inch. Make sure there is enough room to flap wings, my tiel goes into flapping fits in her cage often (just for fun, she's over the night frights), so make sure there's enough room to flap without hitting the wings on the bars. And make sure there is enough room to add many toys and still giving him/her room to move around.
Look around the tiel or cage section and you should be able to find some actual cage dimensions, at least for the minimum size required.
Budgies do seem to be too active for tiels, who are mainly laid back. But my budgie and tiel cages are in the same room and they do enjoy each other's company from a distance. When they are out of the cage they are not allowed next to each other because my budgie pesters my tiel and then my tiel tries to bite him
But they are bonded through just living in the same room together - if they are in separate rooms they will contact call to each other.