Could someone please help me pick one or two styles that would work well for general turning and facing?
Nothing wrong with TCMT inserts. They will work well for steel.
Now for Aluminum, sticking with inserts that will fit in the same holder as your TCMT, I would strongly recommend TCGX *****.AL
These last 2 letters designate the all important "Insert Geometry"
The 'AL' gives you a 20° top rake that works perfectly with aluminum.
I like positive tooling as it works will with thin wall tubing and delicate work. Also uses less power and works well with small machines.
Selecting the right insert for the job and lathe is an art in itself.
The important factor, once you decide shape etc, is the insert geometry.
There are lots of gotchas......
Sometimes you will see a nice looking insert with an advertised top rake of , say. 10°. But on closer inspection the 10° does not start right at the edge but a few thou back. So using this insert on a small depth of cut the actual rake works out to be 0°. So for our purposes, this insert geometry would not work for light finishing cuts. It will work, but you will NOT get the 10° that was advertised.
Try and find a copy of the "Sandvik Metalcutting Technical guide".
Its free and is IMHO the bible for selecting inserts etc.