Ok, first, a simple question: do you prefer option 1 or option 2 in my two posts below?
Now on to some details of where I've got to:
I found a rather obvious solution to placing the bulk of stars in the right position in the galaxy: use a galaxy map as the background. Duh!
I found a rather nice artist's impression of the galaxy, which is shown in the pic at the end of this post. I am using it primarily for star positioning, but I will supply it with the map, in case anyone else wants to use it. I will also supply an annoted version of the background, naming some of the features of the galaxy, such as the spiral arms. It's at the following site, and there don't seem to be any copyright issues with supplying it with my map.
I have had some real problems with getting the scale right. Obviously I know the galaxy is about 100 kly (kilo light years) across, with the core being about 25 kly from Sol, and in my map that means each sector is about 6.25 kly square.
I found my original positioning of the stars didn't actually fit the galactic structure, so I've had to discard it. There's a fundamental conflict between showing on the map stars nearby to Sol and showing the huge scale of the entire galaxy. The basic problem is that if you want to display Alpha Centauri even remotely realistically you're limited to a playing space about 1200 light years across. That's pretty much enough to play "local space" Star Trek, but it represents only 0.15% of the galactic area (I say 'area' because we're in 2D here).
So I'm left with two solutions: option 1 is to keep stars like alpha centauri and Sirius, and fudge the distances and directions. This sounds terrible, but remember that any map representation is inevitably a fudge owing to the need to project it onto the 2D playing area.
Option 2 is to go for maximum realism, within the constraints of what the game allows. In option 2, the nearest star to Sol is Betelgeuse at around 400 light years. This also creates some difficulties. Why would a prewarp human empire scoot right past all the nearer stars and head straight for Betelgeuse? I suppose the answer to that is that the map is only representing the most important 1400 stars in the galaxy, and that Betelgeuse is considered to be the closest star of interest.
Incidentally, regarding the star numbers, I started a 15x15 game with 1400 stars, edited in a further 600 stars, then let the game run itself for 150 game years with the 2000 stars. Didn't have a problem running on my system.