With a PIII system, I doubt that you have a "standard PCI graphics adapter"!
Yes, you likely need updated chip-set drivers.
Start at the system or motherboard manufactures web site.
Otherwise, you should be fine using the Intel INF utility.
http://tinyurl.com/2gtja
Note: the linked driver may not function on Windows 98 first edition.
Without knowing your specific graphics adapter, I cannot verify that DirectX 9.0b is "best" for your system. For many older graphics cards, the driver for W98 does not support DirectX 9. If the driver does not support DirectX 9, both DirectX 9 and IE 6 can cause the system to lock up or have memory leaks.
If you have documentation for your system, it should identify the graphics card or graphics processor chip on your system.
If you don't have the documentation, you may need to open the case and determine what graphics card you have.
If the monitor cable connects directly to a plug-in card, that is your graphics card.
Look at the largest IC on the card.
Note the manufactures name and model information.
If the monitor cable plugs into your motherboard, identifying your graphics system gets a little tougher.
The graphics processor "should be" the large IC nearest the monitor connector.
Again, note the manufacture and model of the GPU.
If this is a name brand system, you should be able to download the latest drivers for both the motherboard and the graphics system from the manufactures web site.
Install the chip-set drivers first.
Then the graphics driver.
Chas