Alright. Galactic structure and formation was my specialty, so we can go as deep into this rabbit hole as you would like. First, this image is your best friend.
Milky Way Annotated

We can't take a real picture of the galaxy because we're stuck inside it, but this artist's rendering for NASA is about the closest you'll get.

So let's start with the basics. Galaxies are ridiculously freaking huge and ridiculously empty. If everything out to Pluto were shrunk down to only 25 mm across, the nearest star would be a similarly sized circle 2 soccer fields away. So some form of FTL travel is a must (my personal favorites are the folding and expanding of space around the ship, and the jump-bubble concept from Traveller).

Anyways. One of the biggest things that will raise hackles from astronomers is to say something like "they've jumped 6 light years. That puts them in the heart of enemy territory!" 6 light years would be like... 2 stars away. At best. If you want an empire that controls, say 50 star systems, you're talking about a sphere maybe 20 light years across. And that's if they own every star within that area and there are no empty areas. Supernovae create bubbles of voids where no stars form. These are usually a few hundred light years across.

As for start types, we're learning that more and more stars could have habitable planets. 75% of the stars in the galaxy are small, red, type "M" stars. These are relatively cool and put out more infrared than visible light. Planets with life could form around them, but they'd have to be close to the star - like closer than Venus. So on a world like this, you'd have a big red sun in the sky and life that likely sees in IR. Stars like the sun only make up about 10% of the total. The really big ones - Class "O" and "B" are rare, making up only about 0.1% of all stars. These ones emit so much x-ray and gamma radiation that even being on a planet really far out won't save you. Additionally, half of all stars are in either a binary, trinary, or higher (mutiple) star system. There are severa l layouts with things like this that work.

Black holes are also somewhat rare. The closest one to earth is 3,500 light years away. However, the density depends on distance from the core. As for habitability in the galaxy, the Mass Effect map you linked pretty much has it down. I swear, Bioware must have had an astropysicist on staff because their science is clean. The closer you get to the center of the galaxy, the older and denser the stars you encounter. Near the core, most of the stars are what we call Population II, an older generation of stars with less metals (read: any element beyond helium). Since they have less metals, these stars rarely have planets. Even if they did, the extra density of stars closer to the center would create too much radiation for life to survive. So on that map, the hole they left in the center area is remarkably realistic. The stars out in the arms of the galaxy have younger, more metal-rich stars and more activity. This is where you get nebulae, the large stars, and lots of planets.

As for names and constellations, you don't need to worry. If you take a look at the NASA map I linked, something like 90% of all named stars and constellations are within that smallest circle - maybe 500 light years across.

The fantastic map I've linked below is the only one I've ever seen that shows the region only a few thousand light years out. It should give you an awesome sense of how void bubbles, nebulae, and other features are laid out.
Galaxy Map 2.0

Whew. That's all I can think of for the basics. I will happily elaborate on any of these points if needed. Hope this helps!