"Far" is not quite the right question which I why I recommended that you read some more. Even in a small aperture telescope, one can see very distant objects - it's just that they will be faint and very unresolved in such a scope. Increasing the aperture means that you collect more light so they are brighter and you increase your resolving power meaning you can see more of the features.
Here is a comparison of a globular cluster - starting from 8" aperture - would you really want to go smaller?
http://www.obsessiontelescopes.com/m13/index.html
Here is someone's impression of a galaxy going from 6" --> 8" --> 12.5"
http://www.clarkvision.com/visastro/...ert/index.html
How much? Well an 8" reflector on a dobsonian mount (a "dob") can be around $400-500 new. Of course, that does not have all the additional electronics, motors & computers. For that, probably $2,500-4,000 for various versions of 8" scope (SCTs on various mounts with various sophistications of alignment and goto software). On the secondhand market, you can make a considerable saving on this and still get an excellent scope.
Cheers
Eric