Sorry but £300 isn't enough money to buy something worth owning for home cinema use, and certainly not if it has to stretch to a screen too.
Projector prices range from <£200 for the toys to over £100,000 for state of the art home cinema consumer projectors. The bulk of the market though is occupied by sub-£1000 projectors. Of those, there's a vast array of business projectors starting from around £250 that are okay for hooking up to the VGA port of a laptop. But they're no good for home cinema because they lack HDMI, and are not widescreen, and they have noisy fans, and poor colour fidelity, and very limited picture performance with video sources rather than data. IOW, you're buying something designed to do a different job. For home cinema they are fish out of water.
The cheapest business projector that'll do an okay job with video is the Optoma H180X. This is around £400. It has a HDMI input and the fan noise is tolerable (28dB). The Eco lamp life is very good at 6000hrs estimated. It's even widescreen 1280x720p 16:9 (native res is 1280x800 16:10). The only caveats are the relatively long throw distance compared to true home cinema projectors, and the basic video processing quality.
The relationship between screen size and projector position is often given as a throw ratio. This is simply one or two sets of numbers that are simple multipliers. If you had a throw ratio of 1:2 then for every 1 metre of screen width then you'd need 2 mtrs of throw distance. Since most projectors have a zoom lens to make the image bigger or smaller then you need two numbers: one to describe what happens when the lens is making the largest image and another for the smallest image setting. This Optoma has a throw ratio of 1.55-1.7 :1 So for a 1m wide image the throw distance will be 1.55m ~ 1.7m depending on the lens setting. A 2m wide image needs 3.1m ~ 3.4m throw distance.
Once you have the throw ratio you can estimate picture size at a given throw distance. The sum is a division: Throw distance divided by the throw ratio. eg. 3m throw /1.55 = 1.93m wide, and 3m throw /1.7 = 1.76m wide
The first of the true home entertainment/gaming projectors are around the £500 mark. The Optoma GT760 is around £550. It has better video processing to get more from movies, TV and consoles than a true business projector. The other thing it has is a very very short throw lens. There's no zoom this time. But this 1280x720 resolution projector needs just over 1m throw distance to make a 2m wide image. You put this projector down between you and the wall/screen rather than sitting it behind you.
If you want full 1080p native resolution as opposed to simply a compatibility mode then you need to up the budget to £600+ The BenQ W1070 and Optoma HD131Xe are both 1920x1080p native. Ball park costs are around £650.
All the above are entry level products in each class. They are not top-of-the-range or even mid-market. So while there may be cheaper general projectors, you're unlikely to find something technically better for the purpose of home entertainment/home cinema for significantly less. They each represent a minimum spend level to get acceptable performance.
Bear in mind too that you'll need a sound system, and probably some cabling (long HDMI as a minimum) on top of the projector cost. On the plus side, these are all fairly bright projectors so you don't need total blackout to get decent image brightness.
I made mine (in my Project - man cave thread)
