Why would you want to connect your brain to the Internet? Far too great a risk of an NSA virus.
What you want to do is place your brain in a networked, Earthquake-proof, fire-proof enclosure, with an Infiniband connection to a Linux server. This would then be linked, via an OpenBSD firewall, to the Internet and also to some sort of ROV that can act as a relay between brain and body.
Meanwhile, your skull would contain an embedded computer, a massive multiplexer/demultiplexer to link up the nervous system and a very high bandwidth microwave link to the ROV.
It would reduce bandwidth requirements and latency if the motor neurons remained in the skull, with the rest of the brain transmitting only executive instructions and not specific nerve impulses. Those could be generated more locally. Split brains are found in squid, so we know this kind of isolation is possible. You'd also need a smaller computer, as it would largely be relegated to providing network security, error correction and data compression/decompression. This means you could increase the number of motor neurons, increasing the sophistication of muscle response.
From the brain-at-home POV, removing motor neurons means reducing distances between the other parts of the brain, reducing response time. (Since microwaves are a fair bit faster than electrochemical chains for transmitting data, latency due to distance is insignificant. You would be limited by signal strength and error correction codes, but the radius would be far beyond typical distances travelled by westerners anyway.)
Dissecting the brain further, with no executive functions in the skull to contend with, eyes could be larger, giving you higher resolution at the same number of distinguishable colours, or more colours at the same resolution. This would require the optic centres to be cut out of the brain and enlarged accordingly. Unlike those parts dealing with memory, the structure of the visual cortex probably won't vary much. By replacing the synapses with optic fibre, you can reduce latency, reduce errors, increase resilience to aging, reduce space requirements and eliminate tau protein knots. The reduced space means more visual cortex for the same response time, letting you process every scrap of available data rather than wasting it as the brain currently does.
Much the same applies to hearing and sense of balance. You could probably double your frequency range and your ability to distinguish tilt.
You may be more restricted in movement, but you would exchange it for superhuman senses and superhuman reflexes.