Adapters - "How far can I go"

[Myggen]

Hello Beloved Argonath Family.
As you see in the title I have a "LONG" adapter problem.
Becuse I dont have no sick 42" screen at my room I wished to use my
22" PC screen. But as I knew from before that I only got the VGA input.
So, I watched around.. Oh, I forgot to say what I need. A HDMI from PS3 to my screen.
Like I was saying, I was watching around for a HDMI to VGA adapter. But they we're expensive
due that VGA can't transfere all the signals becuse it.. Su*k.
And those are not in my money limit. So heres my question. Best to show it:

[PS3}<----HDMI--->{HDMI to DVI Adapter}{DVI to VGA Adapter}{IMBA 22" Screen]

[Kessu]

You should be able to go as far as you can.