You need a new power supply for your HP. Any of the listed above will do. I had/have a HP Pavilion a1730n like yours and I had an 8800GT in it, and it worked great with the system.
can I just use a 6 pin supplementary power connector?...I found they make adapters
If you are referring to using your existing power supply and and just using Molex->PCI adapter, then no. The 8800gt is a relatively power hungry card and the 250-350w psu's that HP uses just aren't up to the task.
With the power supply in there? Go for the Radeon HD7750. Your computer is quite old though and it might not be worth it to put it in there, as it would bottleneck. I would recommend the 6670.
With the power supply in there? Go for the Radeon HD7750. Your computer is quite old though and it might not be worth it to put it in there, as it would bottleneck. I would recommend the 6670.
If you already have the 8800GT then getting a better PSU is something that will still be needed when you decide to change that card for something else.
If you already have the 8800GT then getting a better PSU is something that will still be needed when you decide to change that card for something else.