A reliable deck isn’t really a low-budget purchase. If you’re going to give it enough use that it makes sense for you to buy it, you should probably invest in a new deck with some sort of service plan.
That said, for the low budget route, i’m fond of the Sony GV-D900. I’ve used a lot of them, and you should be able to find them used for around 500-750 bucks.
Another low budget option is using a cheaper camcorder as a deck. The Canon HV30 will do both DV and HDV.
While you can look into HDV decks, which will play both HDV and DV footage, I wouldn’t recommend them, as they would be out of your budget.