Questions about a projector purchase

Hello to all Visualists:
For a long time I would like to buy my own beamer, because I do gigs for parties, exhibitions, installations and the like...
Now I've saved a bit of budget and would like to get a start equipment (which I want to expand step by step).
Here are my thought's:
Since I prefer large-scale projections, I would like to buy a good projector that can make it all of it: HD Ready (should be enough?) Here I would like only a 16: 9 and 4:3 dissolution. It is more important to me that the brightness and the contrast fits. So about 3000Lumen would be appropriate or right? In terms of contrast, I have not quite gone through, since the values ??are often close to each other or totally out of line. In addition I would like to be able to test projections in advance in the future (because it happens too often that I am facing unexpected complications).
The biggest headache gives me the maximum projection distance... With many projectors it is very low, does that mean that if I remove the projector too far from the objects or the screen do I not get the picture sharp anymore? Do I need a wide-angle objective? It may well be that I'm with the beamer 5-6 meters away which would restrict the choice very much.
Even with the brand of the beamers I'm unsure because I do not know how well the different companies process their projectors.
Can you give me any example models you've worked with and which would suite this situations?