What is the best upgrade video card for a sony vgc-ra837gy

Here is a link to the specs for that system.

http://www.docs.sony.com/release/specs/VGCRA837GY_mksp....

The bad news is that is a pretty old system that will not support a real strong video card. The good news is that it has a larger power supply then most systems of that capacity, but it will still limit your choices.

More information is needed, including:

How much memory do you have installed now?
What is the resolution of the monitor you are and will be using?
Are you still using the Geforce 6600 video card listed in the specs?
What is the brand and model of the power supply?
Check on the power supply label and report how many amps of 12v current it provides. Also see if you have one or two 6 pin power connectors.
What are your intended uses? For any games, what games?
What is your budget? (Pending answers to the above, if you want the max the system will handle it might be in the $100 - $150 range.)

For help in defining your personal needs and the system requirements, I suggest you look at the criteria page at this site:

http://www.upgradevideocards.com/criteria.html

You might find some of the other pages helpful to better understand the options and possibilities.