well, your best bet is to recreate it from scratch in Draw. A vector version will be the best format as you can then do both print and web work with it. The "raised" look to it (in this case) can be done in varying ways - either through TheBoss filter or through the Texture/Plastic effect. They do similar things, but there are differences.
You can either use Trace to outline the image and have it create the vector objects, but you'll have a LOT of clean up to do. It would be faster/easier to bring the bitmap into Draw and manually create the vector items in question.
One thing that's going to be a problem, though, is the text "marketing services". That's in an incredibly thin/small/delicate font that will not hold up when you make the image any smaller than it already is. The main text is pretty small/thin, too, for that matter for the physical size you posted.
You need to figure out what's the smallest size it will appear in print (biz cards? letterhead? promotional items like pens?) and design it to fit in that instance. If it works well small, it should work well large. Also, from a printing standpoint, you need to have a "flat" version, too. I.e., make sure the logo will work in one color (black). I mean, you're not going to shell out the bucks for a 4-color print process for something like a pen, mug, other kind of promo items.
If the logo "works" in a single color, you can always modify it later for a full-color process. But just because you have something that works now "in color" with shading, etc, it doesn't necessarily mean that it will work at its lowest common denominator.
Once you have the image recreated in Draw, it's a simple matter of exporting it out to a Photopaint format for any bitmap effects, webwork, etc. You can also do your bitmap effects and bring them back into Draw later on (BTW, i'm not a fan of doing bitmap work within Draw - I always export the image out to the size I'd need it back in print when going to bitmap, then i can do my tweaks and bring it back into Draw without having sizing issues.).
Sorry for rambling on here, but when you have the bitmap in Draw, create a new layer for you to trace on and keep the bitmap on its own layer. With the new layer selected, choose the Bezier tool and click on an object and start tracing. You don't have to be exact here 'cause you can always go back in with the Shape tool and tweak the nodes/lines into the "final" shape. Once you're done, delete the bitmap and save it as your new logo.
Hopefully this makes some sense
