Canon Pixma
iP4700 (or whatever the latest is) is a pretty universal choice.
Combined with some
Ilford Gallerie paper (and the colour profiles they provide on the
Ilford site) it makes for a pretty formidable budget combination.
For the record, I know you mention cheap inks, but steer clear of the non-genuine manufacturer ones (unless you go for a decent continuous ink system, which is unlikely for this number of photos) as they're generally pretty crap, don't last any length of time before becoming discoloured and often have a tendency to block inkjet print heads.