Choose your projector based on the type of optical train you can get

The really important parameters:

2) native resolution 
Ideally 3840x2016 (UHD 4K) otherwise 1920x1080(FullHD). Be careful, a number of advertisements are misleading. This is not because the projector accepts the HD format that it really projects at this resolution.

3) the contrast
1:2000 minimum. Beware of advertising announcing 1:50000 or 1:10000
As more and more projectors use an automatic iris. When projecting stars, the iris is useless! and the contrast falls to 1:2000 or less!

4) black level
The projectors are never able to produce an intense black. There are still large differences depending on models. This setting isn't always well documented and it is a pity. Most of the time, the more the projector is capable of sending level of light, the more blacks looks gray.
Example: choosing a 5000 lumens beamer on a dome of 5m is useless, because it comes at a good level of illumination with 1000 lumens. All we can get with a big black projector is so much slimy gray, instead of a deep black with a less energetic beamer ...

5) choice of techniques
DLP or LCD (LCoS is more expensive)
Prefer by far the DLP, because even with a FullHD LCD, the screen effect is clearly visible, which is really despicable on a dome ...
The new LED/Laser technology seems very promising and is very attractive in terms of lamp lifespan. But not perfect at the moment.

Help for Model Selection

German site www.hcinema.de references most current projectors. 
Main characteristics are:

Auflosung: resolution

Projektionsverhaltnis: projection ratio, determine the choice of condensor. For zooms, the range is variable and could manage to do better adjustments. For example, a range of 1.15 - 1.4 is good for 50mm. A range of 1.6 - 2.5 will be perfect for rodenstocks.

For 50mm, you'll need a ratio equal or lower than 1.4 (but above 1.15).

For Heligon equal or higher than 1.4 (but lower than 1.7 probably).

Ansi-lumen: brightness

Kontrast: contrast ratio (often questionnable)

Schwarzwert: deepest black rate

Sometimes, a projector isn't directly referenced. This is the case with optoma UHD420 for example. But, with a search in the left column for the optoma UHD, we can see that there are many variants, for lamp brightness , but optical train stay's the same. In example, we can use data from UHD40 for the projection ratio.

-Acer P1500 (1080p).
Discontinued.

-Acer P1623 (1200p).
Discontinued.

-Optoma UHD 420X (2160p).
Good results for the low price.

Other videoprojectors could fit. Don't hesitate to help us add models to the list.

Should work as well:

Optoma EH 400+ (1080p).

Optoma WU470 (1200p).

Optoma 4K550 (2160p).

All types of beamers should work if not too much "wide angle". But now, we would recommend:

Optoma EH 400+ (1080p).

Optoma WU470 (1200p).
Brightfull.

Optoma UHD 420X (2160p).
Cheap but with good results.

Optoma 4K550 (2160p).
A must. We regret the focusing variation with temperature variations.

The choice of the projector between 1000 and 2500 lumens seems appropriate in all situations, until at least 6 m in diameter. With 6 to 8 m, 3000 to 5000 lumens is a better choice.