I recently installed an inverter in a semi-tractor, and in the process, I found out a few things about them..
First of all, you'll find that there are many variations and prices for the equipment that is available. There are "true" and "modified" sine wave types of inverters offered, with the "true" type being more expensive, so you may wonder whether there is any advantage for you if you spend the extra money.
One tech article I read listed the following items which they said should be powered by a TRUE sine wave inverter (only)
Fax machine, laser printer, charger for cordless power tools, oxygen concentrators, any equipment which has a variable speed motor, electric shavers, and even garage door openers.
The article stated that it is alright to use a "modified" sine wave inverter to power high end audio/video units, plasma displays (I presume they mean T.V. sets) gaming systems (like your x-box ?) and certain types of (unspecified) electronic test equipment, but they point out that the users of these types of gear generally have a significant investment in it, so why cut corners on the inverter. Also, they stated that some marginal enhancement in picture quality (clarity ?) might be possible with the true sine wave type of power supply, as opposed to a modified type.
After reading that info, I went ahead and opted for the more costly (true) sine wave type, choosing a 2000 watt unit. I use in a Kenworth to power a coffee maker, a charger for my cordless drill driver, some flourescent interior reading lights, and my hi-def T.V. set with it. My picture quality on the T.V. screen is remarkably clear.
Inverters which are 300 watts or less can just be plugged into your cigarette lighter outlet. If you power an inverter any larger than 300 watts from your lighter, you might start popping fuses on your vehicle.
All the larger inverters are wired direct to the vehicle's battery. It is essential that you use some good, heavy gauge wire for this, because the amount of voltage available to power your equipment will be enhanced. For my installation, I went with standard arc welder cable, and used copper connectors which I soldered into place. By all means, you should install an in-line fuse which is rated according to the inverter manufacturer's specs. For my inverter, this was 250 amps. I could not find one locally in that size, so I obtained one from a supplier of solar-powered equipment out of Arizona.
It is a good idea to get a unit with somewhat higher output than what seems to be needed, as Driller was suggesting, that way you have some headroom, power-wise.
You should be allright, as far as staying with the stock alternator on your limo, if all your're running is a T.V. and an x-box. It might be worthwhile to hook up a voltmeter gauge in your limo, if it doesn't have one already.
I hope this will be helpful to you - good luck with your project, NOS..