Your iMac is all of two decades old. So....first of all, congratulations for even getting OpenBSD installed on it, many people tank at that. For your needs I suspect you'll be better off with Tiger 10.4.11. For listening to music just use itunes or VLC, you can still manually enter in radio stations into older versions of itunes. For non HD videos, it should still work if you follow Dronecatchers guide for playing video on low end macs. Search the forum here, he is the master of low end audio and video playback on older macs. You can even download some low def youtube videos in PowerPC media center, convert them if needed. There is also a Russian youtube download site that Dronecatcher and others have gotten to work in as far back as Classilla and OS 9. The site is accessible to older browsers and the video downloads are in MPEG-1 and 2, so easily playable in VLC or Quicktime as long as you stay at 360p or below.
Web browsing in Tenfourfox, set to a mobile user agent will be slow but tolerable for simple websites. I'd make sure to have a hosts file or ublock origin installed. If you can tolerate it, Links2 ported to mac os x by alex_free is a damn fine and speedy browser for older machines. You will need X11. It displays inline images, and pages in HTML 1 so all text is justified left, but it makes the web available to older machines, along with frogfind.com and 68k.news. It also gets you around some paywalls, like nytimes.com and washingtonpost.com for instance. I've even used it to download videos from the russian youtube site, and it worked well.
Here are Dronecatchers examples, note his ibook G3 is a little faster than your imac, but with the Tiger backported mplayer you should, emphasis on should, still be able to playback the right videos. Keeping your expectations realistic is key, as is following exactly what Dronecatcher has done.
http://video.2yxa.mobi (Ruskie download site, change the language to en on the bottom of the page for english) EDIT: site is down for me, hopefully that's not a permanent thing......EDIT 2: Whoops my bad, typo. Site IS UP!