You have received some very good advice.  But Do it right the first time is probably the best.  The projector you looked it as not bright enough for a church auditorium. A classroom setting probably, but not in the big room with normal lighting.  Let me tell you our experience. Oh, and keep in mind this did not happen overnight.

30 years ago we had an old tube type amplifier behind the stage in the church office with 2 clunky mic's.  We replaced it with a transistorized 4 channel amp, then moved the amp to the rear of the auditorium so an operator could see what was happening while running the controls.That'a OK until you get a real musician with stage experience involved.  We went to a small sound mixer with multiple inputs. We learned wireless mic's of that time didn't work well in our building so we put the receiver in a corner of the stage and ran a cable back to the board.

We had some folks who really wanted a projector system.  Dragging our feet and moaning from time to time  (not quite kicking and screaming) we went along.  Our first problem was where do we put a screen?  Typical old church, the original auditorium has been built onto three times and modified and changed and makes it difficult to see a screen from everywhere.  We ended up putting a screen over the baptistry at an angle and the only place it is not visible is behind the big post (like I said, typical old built-on church)  It cost too much money but we got one that rolls up and down at the push of a button.  Take a deep breath and buy one, it is worth it.

The projector was not a lot brighter than the one you are looking at.  It is hanging from the ceiling.  I didn't know it, but you can adjust the display angle (there is a techno name for it) to compensate for the projector not being square in front of the screen. Our projector is 15+ feet above the floor.  The really nice thing is it is almost impossible to block it.  After a while the bulb lost some intensity and we replaced it with a better one.  But you can't just throw it away (we do have a farm background here) so we put it facing the rear wall so the folks on the stage can see what the projector is showing without turning their back to the audience.  One once benefit is turn off the front projector and put the words on the back for folks doing specials .

We eventually built a sound booth in the back corner of the auditorium. It has a huge sound board with 24-32 inputs, amp, wireless receivers, computer with 2 monitors, DVD player, cassette player, video recorder, etc.  A snake runs under the floor from there to the front of the room.  That's a big cable with various cables and wires all bundled together.

Remember this: Whatever you start out doing at some point there will be this new idea to try. "I was at --- and they --- with their system."  You will eventually want to put the word to the songs on the screen.  To do it well you will need a software package and a CCLI license.  Someone will want to show video clips which will require some more expertise.  Memorial Day someone will want to show a collection of photos of veterans. The Sunday after VBS you'll want to recap and show pictures.  Find a kid and turn him or her loose.

Make sure there is a team involved. Even if it is you pushing this, get a team set up.  You could have a farm accident or you could get hit by a drunk on the way home.  There needs to be multiple people working with it.  The guys who set all this up are no longer with our church.  Because of work they guy who was the mastermind behind all this is no longer here.  Affer he left we sat for a couple weeks with no video when about a half hour before church one morning one of our high school boys said "Can I try and make it work?" We had songs on the screen that morning.  Our chief operator right now is a 13 year old girl.  Being honest, the preacher we hired two years ago has more experience with this stuff than any of us and does the set up.  But Kinley produces the photo shows and usually runs the video system during services. Or Grace.  Sometimes Michael, but he's an old guy.  He'll be 40 this year.