Projector

LCD in the right room, with proper light control will look best. Most of the Sony units offer better performance. Getting a demo of a projector is almost impossible so you are left with reading reviews and checking ratings. Your budget is low considering that a quality screen will cost at least $500 and maybe another $200 for the mount. Projectors have not seen the large price declines that LCD's have. So, with your budget I would go with an LCD now and at a later date get a used Sony projector for use with movies. It does not make sense to use a projector for regular TV viewing as the bulbs can get expensive.

I have seen projectors for around $500. Are those good projectors for movies? It's got HDMI connection for my blu-ray player.

I can say that my LCD does not look nearly as good as my brothers DLP.
150 inch is a huge stretch for any projector. I wouldn't believe anyone's claims of an LCD handling this with quality unless you see it in person.
I bought my LCD when I saw the same model in a club playing on 15 foot screens. I'd never use it that large.
The other issue to consider is where will the unit be located. Many units have built in fans. You really don't want a fan above your head.
You really need to see the exact player on the exact screen to be satisfied. The source can be a huge difference too. The last thing you want is to spend $2500 and have a fuzzy screen...

How about saving some money on the screen by using a white bed sheet and glue the sheet to the wall. Next, go to home depot and buy some cheap wood to make the frame around the white sheet. Last, paint the wood frame to black.

Estimating cost: $30.00