not really good for him
His whole budget would be used up with a Sony DSLR and the kit lens, which is a 3x optical zoom. 3x zoom is not what the OP was looking for when he asked for "good optical zoom", which to get good optical zoom would cost him almost or more than his budget to get on a DSLR. Also, all DSLRs have image stabilization when you buy them, whether it's in the lens or in the body.
The one other caveat is that all the lowest priced Sony DSLRs have been hammered in reviews(ie A230, A330, and A380), which is why thy didn't last a year before Sony discontinued them without a replacement.