IMHO, 256MB RAM is too little for 10.4. Yes, it will "work" but it forces Virtual Memory to work a lot, slowing things. 512MB would be a better RAM amount for Tiger. 1G would be very nice. Do "about this Mac" from the Apple menu and, in the resulting window, click "more info." That brings up System Profiler. Click on "Memory in the left pane and that will show you what size modules are installed in the computers two RAM slots. From that, post what's in the slots. That will give the options for adding RAM.
One RAM slot is user-accessible; the other is deep inside and should not be accessed unless you are experienced with Macintosh surgery.
If the computer is used and the drive was not wiped and the OS reinstalled before sale, there could be a lot of deadwood on the drive you can't see--temp files and the like. Review this list of FAQs, especially those dealing with maintenance and performance:
http://thexlab.com/faqs/faqs.html
There is a wealth of info there. The part about "maintenance scripts" can help a lot on an old machine.
A too-full hard drive can slow things. Do "Get Info" on the hard drive and see how much space is available for use. You need a minimum of 10-15 percent free to keep OSX happy.
If the external hard drive is USB, it will never be satisfactory on a 700mHz iMac except for occasional backing up of smaller files. That modeliMa has only USB 1.1 ports --dreadully slow. Your only option for speed with an external drive is FireWire. You have the ports.