OS3.9 was really intended for a maxed out Amiga with a graphics card as the high color icons use a non-standard display engine, IIRC. You can, of course, convert all the icons back to standard 4 or 8 colors one at a time. GRIN.
Maximizing ram would be high on my list. The MB can be expanded to up to 16 Megs of fast ram using zip chips (still findable). The DKB 3128 allows up to 128 Megs in a Zorro III card, but these are very rare and there is a lot of competition due to collectors. A non-GVP accelerator with ram expansion would probably provide the greatest bang for your bucks (GVP uses hard to find, proprietary ram).
You should now be able to select any of the standard ECS resolutions with Prefs/Screenmode if the drivers are in DEVS/Monitors drawer, IIRC.
You have good options available for ZIII cards for graphics, ethernet, sound, etc. Since the A3000 already has a built-in flicker fixer, you don't have to compete for a Picasso IV card. I would shoot for Picasso96 (Retargetable graphics driver/software) compatibility. The package lists supported cards and is available on your 3.9 CD.
If you want to play Mp3s and streaming audio, I've had excellent results with MasPlayer, but there are retargetable sound card available too.
Hang out for awhile and see where others have gone. You arguably have the most expandable Amiga model. Many of us are proud of our machine's relevance today. Some of us use Amigas for nearly everything. That's not bad for a 17 year old machine.