K6 GSX-R1000 owner here. Bought my bike in 2009 on 3809km, it's now sitting somewhere north of 50k km. I service my bike myself (no warranty to void) and have since I bought it. I've only ever had to replace tyres, brake pads, batteries and front fork seals (and iridium spark plugs, like once or twice or something) as non-service items. Only issues I've had is the pair valve which I deleted. The motors are basically bullet proof. Although, I don't think my bike has had a hard life.
Normal servicing items are usually oil and oil filter. I have a washable/reusable BMC filter and the iridium plugs last very long- I'll probably check them to see if they are within spec for the next service, doubt I'll be replacing them though. My bike is due an annual service so I'll check what the servicing costs are against what needs to be done at the next service (if you're looking for dealership pricing on services, that's a nope from me). There's a valve clearance check in there somewhere that I had done, but it was a few years ago and I can't really remember what I paid for it- it's one of the few things I don't do myself. It wasn't too expensive though and I think it's something would have be done on most bikes anyway.
From what I can remember, the GSX 1000 uses the old k5/k6 motor (or maybe a slightly retuned version of it, not sure on the details) unless they've changed that with the new GSX- I haven't been following the development of the GSX to be honest.