$1K should be fine, and I think one of the Panny digital receivers might be a good choice too. Once you are done with that, I'd probably shoot over to
HSU and check out the VT-12 + STF-2 or STF-1 package. That, plus shipping and your receiver will likely be just over $1K, but should be a very good starting system.
Not sure about the TiVo remote, but if it isn't programmable, you aren't going to be able to use it for everything. I'd look at a nice programmable universal remote like the Harmonys from Logitech.