All this depends on what you intend to do. If you want to play games, the 8300GS is fairly weak by today's standards. Of course, integrated graphics rely on your RAM and CPU to do the work, so that's pretty weak too honestly.
Budget wise, there's some fairly decent cards available pretty recently. What you should buy (if you choose to) really depends on whether you wish to play games, and what monitor resolution you have.
You could get a basic ATI 5570 for $70http://www.newegg.com/Product/Product.aspx?Item=N82E16814131343&cm_re=ati_5570-_-14-131-343-_-Product
nVidia's most recent card: GT430 for $70http://www.newegg.com/Product/Product.aspx?Item=N82E16814500176&cm_re=gt_430-_-14-500-176-_-Product
These are what I'd call "Budget" cards. Here's a good review that compares the two directly:http://www.anandtech.com/show/3973/nvidias-geforce-gt-430/1
Now, if you want better performance, have a higher resolution monitor, or have more money to spend, I'd step things up.
The GTS 450 and ATI 5770 are good cards to look at in the next price/performance bracket.
Can you give us more information on the rest of your PC's specs? Processor, RAM, operating system, power supply model?