Some general electricity questions (relays, etc)

I have a 220W Power Inverter, switching from 12V DC to 115V AC (I think
that's standard, reguardless, not important...) Attached to that Inverter
will be a computer's power supply, which is rated at 200W (which means
it'll work just perfectly with this inverter, and it does, I've tested it
plenty of times before). But here's where my problem arises (haha, I said
"rises")...

The inverter has an on/off switch, which means if I leave it on, it'll
kill my battery(s). So I thought of lopping off the lighter plug bit and
just hooking it up to a relay. Then have the relay run directly to the
battery and the SIGNAL wire run to my ignition or some happy *********
like that (again, not important).

But..... I don't know what kind of relay to purchase. I found a website
called www.digikey.com that has everything known to man there, including
all types of relays. The only variable is the Amps.... so now to my actual
question...

What amperage should I get for a Power Inverter that's hooked up directly
to the battery? Would that be listed on my battery? Since I have TWO
batteries, wouldn't that change? Also, when set in parallel, extending the
wires increases resistance, which makes things superhot, so again,
wouldn't that be a factor? ******* electricity...

Remember, I'm going from DC --> AC, so the final product (in this case the
computer) doesn't matter. I only need to know the load that the relay will
be inputting... or something like that.</pre>