Hi Stavros,
I'm pretty sure most Tv's will remember the input setting after turning off but where you might run into trouble is if you choose a tv that won't power up without pressing the on button after shutdown. As an example, if there is a power outage and everything turns off, you might have to access the tv to turn it back on again after the outage. With the Sony Wega I have it stays in the ON position so when power comes on it automatically turns on.
This is also important because on my Power strip everything turns on and off through my PC......when the PC turns off EVERYTHING goes off and when it goes on...EVERYTHING goes on. So if you have a TV that doesn't stay in the ON position you may have to keep turning it on everytime you shutdown.
I'm no expert in this, it's just stuff I have read through forums. It's also easy enough to test a TV out on this before you buy it. Kijiji is a great resource, I got mine TV for $25. I went to the guys house plugged it in, set it to S-Video then pulled the plug. Then I plugged it back in and it came up back on S- Video, I didn't need to press POWER it just turned on again as soon as I plugged it back in. Bango perfect TV for Arcade!
Kevin