Lasurstern looks like its gorgeous from some of the pics I've seen on here! Now, I wish I got that one instead of my Franziska Marie whom has never bloomed yet in her two years in the ground. I think that's a great choice!
As far as how far from the rose, I've heard some say a foot or two away. But, others may have better opinions on that.
If you do a search on this forum for Lasurstern you'll see some pics of it, what a beauty!

Colors are very subjective and "best" is always a matter of opinion but I'd consider 'Lasurstern' more of a lavender-blue rather than a true purple. But I guess it depends on the effect you are looking for :-) It would look great growing amidst a bright yellow rose (btw, did you mean 'Graham Thomas'?.....I've never heard of 'David Graham').

I prefer some that have a darker, richer color - 'Etoile Violette', 'Gipsy Queen', 'Romantica' or 'Negritjanka'. And there is the always popular 'Jackmanii' or 'Jackmanii Superba' - not quite as intense but very reliable and very floriferous. In my previous garden, I had 'Etoile Violette' growing through my 'Graham Thomas' rose and it was a stunning combination.

I've attached a link to a previous discussion on this forum about purple clems.....maybe that will provide additional choices.

And if you are planting both the rose and the clematis at the same time, you can plant them quite close together - in the same large, enriched planting hole if you like. Otherwise, you will need to allow sufficient distance so as not to disturb the rose's root system.

Here is a link that might be useful: purple clematis

Lasurstern is not a very strong grower or bloomer for me in Chicago, though we have a short growing season with lots of humidity. For easier growing purples, I'd go with ones recommended like Jackmanii, Etoile Violet, Romantika, Blue Belle, Warsaw Nike. Much better choices.

That's a tough one, almost like asking what's the best purple wine. I have quite a few clematis in my garden, including many of the ones mentioned here, and I have to say that, for me, nothing can beat the gorgeous-in-every-respect Jackmanii. Gary