need advice to purchase the right PJ

Quick answer based on your usage: Viewsonic Pro8200. It's right at your spending limit. It's a light cannon and will have no problem blasting a bright, colorful image on your wall, during the day.

The Viewsonic Pro8200 or Acer 6500 are the only 1080p projectors in your price range, otherwise look at the Benq w710st.

If you were willing to spend a little more, here is a comparison I did of the various projectors.
http://www.avsforum.com/avs-vb/showthread.php?p=22026149#post22026149

Some of the comparison I did not have them ALL in my own room, and the Benq and Optoma I only saw briefly, but I did own both the Mits hc4000 and the Viewsonic Pro8200, so those I have > 1000 hours on.
The Mits hc4000 is the best DLP overall under $1500, but it isn't bright enough. The w1200 is the best bright DLP under $1000 if you DONT do any gaming, but it is still slightly more than you wanted to pay. The Pro8200 is a good projector, but does have a few annoyances as all projectors do.
Edited by coderguy - 6/7/12 at 10:05am

Also see my master comparison from my signature (although not a lot of info in there about sub-$1000 projectors).

For a sub $1000, the main factor is if you want 3D or not, and if you game or not. If you want 3D, then you'll be limited to 720p units. Although there are refurbished Optoma hd33's running around $1200.

Optoma GT750 if you want 3D and game (I'm not sure this is the best 720p 3D one, but it's popular in the forums).
If you don't care about 3d, then the options are much more numerous.

Benq w710st if you want the best cheap 720p projector with the best OVERALL image quality. I am not sure what is better for gaming, the Optoma GT750 or the Benq w710st, as I have never seen the two compared.
There are fewer reviews and comparisons in the sub $800 projector range than there are on more expensive projectors.

If someone is going for the best overall 2D projector that can do everything (sports, gaming, movies), then the choice is the Mitsubishi hc4000 (but it is not as bright as some of the others).
If someone is going for the best overall BRIGHT movie image under $1000 and does NOT do any gaming, then the Benq w1200.

Otherwise, for under $900 and 1080p, there is only the Optoma hd20 and the Viewsonic Pro8200. The Benq w710st should beat them in contrast because it has an IRIS, but those are higher resolution.

If it were me, I'd definitely give the Benq w710st a hard look, as it does many things well, but the one drawback is more rainbow effect from the slower color wheel (only if you are sensitive).

Well if you need lens shift, then your only option is a refurb Epson 8350 or an Acer LCD. I haven't seen the Acer LCD's, but I'd pretty hesitant and would stick with Epson. Not many projectors under $800 are going to have much lens shift.
There are a couple Epson 720P LCD's under $700 that do have lens shift.
Edited by coderguy - 6/7/12 at 9:52am