Hi Splat, that is exactly the type of shim that I used (except in the "B" and "C" sizes - depending on which machine and the size of the foot). You will need an assortment. The kit comes with a range of thicknesses so that you can achieve 0.001" resolution up to about 0.15" with only a few shims (you don't end up with a whole stack of cards). That may end up costing a bit (I am able to collect cast off shims from work, since the guys generally don't bother to clean and resort old shims). Of course, you can save a bit by cutting flat bar instead of using the shim material for 0.125 (or any other standard size).
Bob is quite correct that you don't need to exactly level the lathe. I find it is a good starting point, then tweak a bit if it isn't quite cutting straight (if it is way off, then twisting the bed won't solve it - you have to figure out what else is wrong).
Another approach which works well is to make yourself a set of stand up blocks. Especially if you want to raise the machine up a bit. Use 2.5"ish round bar (say 1" thick) under each foot. Then you simply trim the length of each one until it is level (or twisted a little). Of course you use the lathe to do the trimming (facing), and you can use feeler gauges as temporary shims as you are figuring out how much needs to come off each corner. There ends up being quite a bit of back and forth, temporary blocking and so on, but if you have some good sized scrap bar (most any material would work fine) - then it is very cheap. The previously mentioned beverage container material could also be useful for additional fine adjustment.
I suppose you could make the block almost any height that bought your machine to the correct elevation (depending on how tall you are). Anything taller than the bar diameter I'd drill and tap so it could be bolted to the base of the machine