I owned a Mini-14 Ranch rifle for a while. While it was nice, light, and cheap (I think I paid about $450 for mine) it did have some shortcomings:
It's a bitch to clean.
The trigger is so-so.
Mags are more expensive, harder to find, and a bit tougher to fit into the rifle.
The accuracy is not great.
The barrel is thinner than most AR barrels, which causes it to heat up quicker, degrading accuracy. Furthermore, a thin barrel "whips" more than a thicker, stiffer barrel.
The AR system has many advantages over the Mini-14:
It is a modular weapon system - you can trade upper receivers simply by pushing out two pins. Thus, you could go from a 16" barrel to a standard 20" barrel to a 24" competition barrel easily.
Magazines are cheap, plentiful, and (as long as the brand is chosen with care) reliable.
It is much easier to clean.
There are an incredible amount of aftermarket accessories to customize your rifle.
I sold my Mini-14 to a friend a while back and used the proceeds to buy a pimped-out Ruger 10/22. I own two ARs and love them both. A Bushmaster is in the neighborhood of $750, I believe. If name brand is your thing, Colts are a bit pricier.
If you are even a bit mechanically inclined, you can buy the stripped lower receiver and build one yourself. It is not difficult, and will take about a day to assemble. You will save about $100-$200 by doing it yourself. I have put three together, and as one who is not especially mechanically savvy, I tell you that it can be done.
Bottom line - spend the extra bucks on the AR. You will be much happier in the long run.