Back of the napkin type calculations... assuming 90% efficiency in your inverter.
120V, 90W = 0.75A. Allowing for the inverter inefficiency, calculate for 0.8333A at 120V (0.75 / 0.9).
120V / 12V * 0.8333A = 8.33A. So for two hours use, you want 16.67Ah available. Assuming you're buying a deep cycle battery, at 50% use, you could get away with as small as a 33AH battery. Kind of rules out the Radio Shack variety - you can get very small 12V/18AH deep cycle SLA batteries here in Oz for example - this usage could be drawn from the battery, but flatten it in the process and shorten it's lifespan.
375W inverter sounds fine - if you get a smaller inverter, eg 100W, they get hot and they can cut out even though they're "rated" for the load.
Charging deep cycle batteries is another issue, which is why I mentioned AGM batteries - they're much more tolerant to casual charging without the need for stepped voltages. Might be a good idea to drop into a solar forum and put the same question to them and see if you get a similar answer - this is an area I've done a stack of research on, but haven't actually laid out any cash yet (was looking at dual batteries in a 4WD for running a camping fridge etc). You could also get better advice about whether modified-sine is appropriate for the TV/DVD.