I have two (as I have the 2 male budgies) of the usual clip on type birdbaths, that just sit on the grate on the floor of the cage. I use them as seed dishes. It gets them using the bottom of the cage, they cut down on the scattered seeds/hulls and the bath roof is a good poop protector.
For bathing, I use a shallow steel dish on the floor of the cage each morning. If I left it there, they'd probably drink from it.
For drinking water, I previously used the type CC linked but had issues with them leaking. I added open dishes for a while. I considered the rabbit/rodent style bottles but have had issues with the little ball jamming with a pet rabbit in the past. I am currently using two of these:
(Touch wood) so far, they have been great. Never leaked. I know that stainless steel and glass are considered more hygienic than plastic, but this bottle is at least made with curved seams so no nasty joints where germs tend to accumulate. Only suitable for vertical, budgie sized spaced cage bars though.