Square wave will be cheaper and easier... but what on earth do you want 10A at one volt for?
Realistically you'd use a DC-DC converter to get you 1V (ish) at DC, then use 4 heavy-duty transistors (probably MOSFET) to give you switched square-wave ac.
If it's going to be lightweight, you'll use the DC-DC converter running at several tens of kilohertz, and it'll use a ferrite-cored transformer internally.
Rectifying the ac in the output of the DC-DC converter (1volt-ish) will be horribly inefficient because you'll be dropping half a volt (ie half your final power) in the diodes. Euurrrghhh! I guess you get special low-drop diodes - they must use them in computer power supplies since modern microprocessors use many amps at around 1V. You could probably learn some relevant tricks from looking at modern computer PSUs.
You won't be able to make efficient use of this 1volt with electronics, so I guess you want to use it for a motor or tungsten bulb or something?
But a bulb wouldn't need AC, and an AC motor powered by a square wave would judder like crazy, sound ghastly, and possibly shake apart its bearings and anything mechanically coupled to it.
If there's some connection to aircraft, why use 300Hz instead of 400Hz? They'll be no cost or complexity difference.
If you are new to electronics then this will be a very ambitious project. You might be able to get a 12V to 1V DC converter "off the shelf" (probably from a Chinese supplier), but I reckon the 300Hz AC bit is non-standard enough that you'll have to roll your own there.