As you don't need a loud or fast instrument a fairly basic English with concertina reeds (second hand) would be affordable. You don't even need a plush metal ended or raised ends model. Plastic buttons would be fine also. I'd keep a close eye on Ebay for one in playable condition and have it serviced. Generally speaking English are a lot cheaper, type for type, than Anglos. I agree with Dick, accordion reeded steer clear of. I accompany my singing with anglo and melodeon, but for singing I often wish I'd started out with English. The chords are much more friendly and logical.
A duet system, Crane, McCann, Jeffries would be an alternative but cheaper models are very scarce, non-existent in the case of Jeffries.

If you're stateside there's always a Chemnitzer but they're accordeon reeded, although well-made.