Do it yourself. It's really very easy.
Engine should be warmed up first so the oil will flow easily when you suck it out. Before proceeding, get a rag or small pan to catch dripping oil from the filter when you remove it. Begin by unscrewing the black plastic cap from the oil filter canister located on the driver's side of the engine compartment, near the windshield. The nut on top of the cap is a 36mm. If you don't have a socket that big, you can use an adjustable wrench; just be careful it doesn't slip. When you remove the cap, which has the filter attached to it, most of the oil will drain back into the oil pan but some will remain in the canister. Unsnap the old filter from the cap by pulling on it. Now pry off the large O-ring which is located in a groove near the top of the cap and replace it with the new one that came with your oil filter. Use a little oil on your finger to lubricate the O-ring so it has a thin coat on it.
Now snap the new oil filter onto the cap and make sure your hear it "click" in place. Now use your oil evacuator to suck out any remaining oil in the oil canister, then pour in enough new oil to fill the canister about half way. BMW skips this step but I want the oil system to get pressurized as quickly as possible when starting the engine so I like to "prime" the oil filter canister. Now put the cap with attached oil filter back into the canister and snug it all the way down. Keep an eye on the O-ring to make sure it doesn't get pinched. Now pull out the dipstick and stick your oil evacuator's tube down into the engine's sump until you feel it bottom out. Suck out as much oil as possible. Remove the evacuator's tube, put the dipstick back in, and fill the engine sump with Castrol 10w60 oil until the dipstick indicates you are at the minimum fill level. Now start the engine, make sure the engine oil light goes off quickly, check to make sure no oil is leaking from the filter canister, let the motor run until the temperature gauge indicates normal operating temp has been reached, then turn the engine off, wait about a minute or so, then check the oil level again on the dipstick and fill to maximum level (do not overfill!) Pat yourself on the back.
As far as the copper washer in the oil filter kit is concerned, I have a 2001 and a 2003 Z8 and neither of them has a bolt holding the canister lid down. My lids have a 36mm nut on top which is a molded part of the cap. I checked the BMW service manual for 2000 model Z8's to see if the earlier ones had a different set up but it showed the same setup I have. Perhaps someone with an early car can confirm that they have a different oil filter canister setup than the later cars. As far as I know, the copper washer supplied with the new oil filter is to be used to replace the sealing washer on the oil pan drain plug. Since you are sucking the oil out from above, you don't have to remove that drain plug so the washer is superfluous. And, since there have been reports of stripped drain plugs on Z8s, I think this method is the best way to go.
Hope this helps!
Grease Monkey