Welcome.
As you may or may not know - tires and oil threads can become somewhat of a "religious" argument on motorcycle forums, so we usually constrain these discussions to the "Rants, Tires, Oil" subsection. But, we've had plenty o useful discussions on these things in the past. I'll attach a few threads I found using the search function, below.
What year/model R65 do you have? Most likely it is not an LS-model (which has different wheels) and uses the usual 18" cast allow 'snowflake' wheels. There are a number of good brands/models of tires that will do the job, depending on your tastes and budget and type of riding.
First off - you should be using tubes. These cast wheels weren't designed for tubeless application and don't have the proper "hump" on the rim to help retain the tire bead if the tire deflates - the valve stem hole is also not designed for a tubeless stem. There are some people who will say that running tubeless is OK with these wheels and they get away with it. That is just an area where we tend to "agree to disagree" and move on. But, the official BMW position on these are to use tubes.
Next point/fact - you can use tubes in any tire -just because the tire is rated for tubeless doesn't mean it cannot be used with tubes. It can.
The original tire sizes are 3.25x18 (front) and 4.00x18(rear). You can still buy some tires from some manufacturers in these sizes if you shop around. But, there are also many tires in "metric" sizes which work perfectly well. The thing to know in the "metric" sized tires is that the sizing isn't all "exact/uniform" when mounted. One brand's 120/90x18 tire when mounted on your rim may be 119mm wide and not rub on the swingarm - another brand's 120/90x18 tire when mounted might be 124mm wide and will rub. The fact is that the RATIO of width/height on these tires is always correct (120/90) but the actual physical measurements can vary. PArt of this is due to some variations in the nominal wheel rim width that the manufacturer uses/specifies for mounting the tires on. Some manufacturers do a good job of specifying min/max rim widths for a given tire size, some do not.
In general, most metric size tires will fit most easily on the snowflake rims if you go with a 90/90x18 front tire (or possibly a 100/90x18, but no larger) and with a 110/90x18 rear tire (some 120/90x18 tires will fit, but some won't). Also, a number of the 120/90x18 rears may require you to at least partially deflate them when putting the rear wheel on/off for doing other sorts of servicing - this is a hassle in my book and I avoid it.
All this said, I run Bridgestone BT45 tires on my R65LS - a 100/90x18 front and 110/90x18 rear. The LS front rim width is a little wider than the snowflake front rim width, so the BT45 100/90 size fits OK and is within the manufacturers spec for rim width in that size. The also offer a 90/90x18 that should be fine for the snowflake. Another popular tire model is the Spitfire S11 tire that also works very well on these airheads. And, there still are the traditional Metzlers - though I've migrated away from them myself over years of airhead riding. Avon AM26 Roadriders are also popular with airhead riders.
Some folks have installed Kenda tires for offroad riding - I think the K270 model comes in 4.00x18 , but again, you will have to be mindful of possible clearance issues, both at the rear swingarm and fender clearance for the knobs, and under the front fork brake/mudguard mounting bracket for whatever you put out front.
Here are a few threads that may help-
http://www.bmwr65.org/cgi-bin/yabb2/YaBB.pl?num=1313937611/9#9http://www.bmwr65.org/cgi-bin/yabb2/YaBB.pl?num=1260644197/28#28http://www.bmwr65.org/cgi-bin/yabb2/YaBB.pl?num=1250387641/7#7http://www.bmwr65.org/cgi-bin/yabb2/YaBB.pl?num=1371615149/1#1