As mentioned, a dial indicator is necessity if you intend to do any serious lathe work. As for the style of holder I think a magnetic base is more than sufficient. I use them for indicators on the mill, surface grinder, and lathe.
Rather than buy an unheard-of brand indicator I would check out the listings on eBay. Over the years I've purchased several excellent quality name brand ones there at prices at or below the asking price of the one you linked to on Amazon. In time I believe you'll find you need more than 1 indicator, especially if you intend to work in both metric and imperial measurements.
I now have well over 2 dozen indicators and close to a dozen stands in the shop. Imperial indicators include ones that measure in increments of .0001", .0005", and .001". The higher resolution ones have a smaller measurement range. The lower resolution ones have a measurement range of up to 2". The higher resolutions are used for more precise measurements while the lower resolution ones come in handy when needing multiple diameters on a single part.
Metric indicators include ones that measure in increments of .002mm, .005mm, and .01mm.
Here's a picture of some of the indicators in the shop. Since this was taken, I have acquired a few more metric ones, and a few more magnetic bases.