[verb (plain)] + んだけど / んですが [i-adj] + んだけど / んですが [na-adj] + な + んだけど / んですが [noun] + な + んだけど / んですが
んだけど sets out the situation first and then asks, suggests or tells: "I'm moving tomorrow – could you help?". It is the explanatory んだ plus "but", and it follows the plain form, with な after a noun or a な-adjective. んですが is the polite form.
The second half does not contrast with the first. The first half is the reason the second half is being said, which English joins with "and" or a pause rather than "but".
A noun or a な-adjective takes な, not だ.
The sentence can stop at んだけど or んですが. You lay out the situation and the listener works out what you want.
When the second half goes against the first, the けど is an ordinary "but", and the ん still marks the first half as background.
んだけど is for friends and family. んですが is polite and the usual choice with strangers and at work. んですけど sits between them: polite, but softer and more conversational than んですが.