Bandwidth to/from Mars wouldn't be too bad with enough power output. Latency is the big problem.

So I think there will be massive caches on both sides. Accessing any popular content will be pretty fast because it will already be cached. Live data will be delayed by up to half an hour depending on orbital position, but that's not terrible. Conversations would be the worst, with up to an hour delay round-trip.

Past Mars it would get harder. You'd need much more power to keep the bandwidth up, and the latency would get worse.