as for space.. i'd just go with a via board. You really don't need the power unless you want it. Space will get tight very thick. I was in your spot when i started way back in the day. i got a mini-atx and now i want to upgrade to a mini-itx.
The problem with an inverter is that once you crank your car it'll turn off and turn off your computer. Thats why people like a dc-dc PSU.
As for the screen. Think long and hard on this. Plug your computer into the your TV and see if you can deal with the text being blurry like that. If you can't stand it then spend some cash on a VGA screen.. you'll be happier in the long run.
Lots of people go without a HU. They just run their audio right into an amp.