When installing Windows 98SE using the setup floppy (boot disk) there is no information written back to the floppy so nothing is carried over to the next install on another system from the floppy.
All Windows 98SE CDs should be bootable even the upgrade CD so you can install from CD.
Please don't over look the value of the chipset drivers and Windows Update.
The motherboard chipset drivers are necessary for the AGP slot and IDE controler to work properly.
Windows Update. off the top of my head , the one I know you will need is the "Windows IDE Hard Drive Cache Package".
http://www.microsoft.com/windows98/downloads/contents/WUCritical/q273017/Default.asp
"During shutdown, data from the cache is written to the hard disk for storage until the computer is turned on again. During a typical shutdown process, any data written just before shutdown may still reside on the hard disk's hardware cache. Older processors typically execute the shutdown code slowly enough that the hard disk's cache flushed the written data to the physical media before the machine lost power. As processors have increased in speed, the shutdown time has decreased to the point that data may still be in the hardware cache when a computer is turned off, and that data may be lost. This increased processor time, coupled with the fact that hard drive caches have increased in size further increase the chance of data loss."
Run scan disk to repair any errors on your hard drive before and after you install the "Windows IDE Hard Drive Cache Package".
A8V Deluxe; chipset used, VIA K8T800Pro VIA VT8237
http://www.viaarena.com/default.aspx?PageID=2
"Win95/98/98SE are now relatively old operating systems, and latest release drivers are no longer optimized for those operating systems. Many users of VIA chipsets who run Win95/98/98SE report that using this old 4in1 version, they experience a more responsive system. If you add new hardware or peripheral devices to your system, however, and you experience instability or find that a new peripheral device does not function correctly, update to the latest VIA Hyperion driver package which may contain updates that will increase compatibility. Also note that the inf file version in these drivers (which contains chipset IDs) dates from late 2001. If you are running Win98SE on a system from 2002 or later, you will require later release drivers so that your chipset is properly identified."
I have not installed Windows 98SE on anything in so long I would have to refresh my memory of all the updates needed.
It would be best to allow Windows Update to install at least all the critical updates for Windows 98SE..
P/S
"grotty old windows 98se left over from the last pc"
Is this a retail or OEM version of Windows 98SE.
If it is a restore CD from the old PC it will not work properly on your new PC.