First of all, you do not want a 'hammer drill." You want either a 'roto hammer' or 'demolition hammer.'
The Roto hammer will need to be large enough to take either SDS-Max or Spline bits. (Spline drive is pretty much out of favor). If it's a demolition hammer, it will have take hex shanks, either 3/4 or 1 1/8".
For the money you want to spend, and the relative rare use the tool will see, I suggest you consider the Harbor Freight offerings. Tool snobbery aside, I have found this "Cheap Chinese junk" to perform quite adequately in these particular tools.
If your area is particularly rocky, or you also need to take apart post light bases, I suggest you 'up the ante' to about $900, and get Makita's 35# (half size) jackhammer.
While any of these tools will drive the rod without using a bit, I always use a bit. I see no reason to risk the tool by not having a bit in place. Ground rod driving bits cost about $60.
I have a Hilti TE-75 that I bought used off of e-bay for $475 plus shipping. Bought the bit to drive ground rods with and never regretted it. Wont drive one thru rock, but not much rock around here anyway.
Life is tough, Life is tougher when you are stupid