For many like me, it is a hard question to answer. I started in the digital world so I was already in possession of high-end pigment printer, so I never did have first-hand experience with a cheaper, lower-end printer. But that is not to say they won't work as digital negatives precede the advent of pigment printers. So many early adopters cut their teeth with dye-based printers like the Epson 1280. In general dye-based printers have lower UV opacity than the pigment printer, the latter also being more expensive. The UV opacity affects the Dmin of the print. Different processes require different levels of UV opacity in order to get cleanest highlights without staining. So the choice of printer is governed from the technical perspective of what processes you are going to do, apart from the purely economical one. The traditional or classic cyanotype is probably one of the least demanding of the processes in terms of UV opacity (particularly processed with plain water) so if that is the only thing you are going to do, at least in the beginning, many of the good photo-printers within your budget might just work fine. May be someone with direct experience will chime in with exact models.
Regarding the printer you have, chances are that it is not able to properly "see" the media when you are trying to print the transparency. Try using a plain paper as a carrier sheet underneath the transparency and see if that works. The roller marks are probably just rubber rollers transferring some of the accumulated ink on to the sheet. Try cleaning them with some sort of alcohol-based cleaner. I doubt this printer has the "pizza wheels" like some of the high-end Epson printers. If they are "pizza wheels" like Alan said, the solution if at all would be complicated. If you can show a picture, we would get a better idea.
:Niranjan.