I haven't read everything, but if you are not replacing your countertop at the same time you are limited by your existing countertop. You need to find a sink that fits the same template and the basin fits in the same cabinet footprint.
If you previously had an over-mount sink and are keeping your counters, you likely need to buy a new over-mount sink as the counter edges won't be finished properly to install an under mount sink. Under-mount sinks can typically only be installed in solid surface countertops (granite or quartz NOT formica or tile) due to the need to have a finished counter edge around the sink.
I do not live in a family where every dish gets cleaned every day after every meal. I like having a sink with two basins so that dirty dishes can be in one and then I still have usable sink space left for other things, washing hands or veggies or draining off boiling water etc.
I have never had anything other than stainless so cannot comment on that.