Well, since this is purely theoretical, I will go with it being small and unobtrusive (possibly just a small device the size of a modern phone, but possibly a wristband or something of similar size). It would wirelessly sync to a brain-computer-interface (I imagine it similar to a hearing aid, in that it clips on to your ear around behind, but not in to your ear). It would use non-invasive attach its self to your brain (imagine it as being controled as you would a limb, and it would be just as natural (and yes, i know we have this technology right now, so no need to tell me!)). Its 'screen' would be viewable in the same way you can see from your eyes, it would simply be another sense for you to interact with.
I would require the device to have decent processing power, in order to at the very least keep up with my brain. And a lot of high speed memory (preferably remote), so that I could save and recall large amounts of data. A very fast wireless internet connection (Future-G network) would be required.
As for applications, I would imagine the device would only come with an operating system, which would contain an AI that I could ask to simply create an application to suit my needs at the time (although, I would not ask in that way, I would simply as the AI to do it). For example "AI, I need to sort through this jungle and find any new beetle species, and then immediately consult any databases, and send findings back to my lab".
Almost instantaneously the AI would program a visual searching program, that could cross-reference with databases and even negotiate network connections through to my lab. I envision that in the future the concept of an application will be redundant.
Some other features I would like to have (although I acknowledge that they could be potentially dangerous) would to be to allow the BCI to interact with my sense and brain, such that it could write a movie to memory, or add some kung-fu skills, or even give me a heads-up-display on to my vision, or change it to IR view or thermal. Also, it should be able to interact with my hearing, so I could listen to metal very loudly without having ear drum damage (since it skips straight to my brain).
I think that would be pretty much as close to perfect as I could get. Oh, well maybe if it was a DNA computer, engineered to be a cloud computer, simply injected in to my body, thus requiring no power, pockets, or anything. That way it could also monitor my health!