When you say you have a grinder for sharpening tungsten, are you talking about TIG electrodes? If so you won't want to share sharpening jobs with that, it will contaminate the tungsten.
I have a 1hp 8" grinder, that has done a decent job for grinding HSS tooling. There seems to be a preference for using a 2" belt grinder though.
There is a monster HSS tooling thread here. It might take you a few days to get through it, but I have found it very helpful.
Models for grinding HSS lathe tools
There is another much shorter thread on boring that you may find helpful as well.
A Boring Primer
As far as inserts go I have a 5 piece basic set that uses triangular inserts. It came with my 11" lathe so I wasn't involved in choosing it, but it works well. I mostly use the LH, RH and center tools. I have a (cheap) set of brazed carbide boring bars, that I chose for the price, and an insert flycutter for my mill. I have only dabbled in inserts, mainly for finding replacement inserts and wow is that a confusing system. Not just one either there are two different sets of identification codes out there. One thing I have learned is different shapes give you more or less replacement cutting edges for wear / screw ups. My triangular inserts basically give me three edges before the insert is done. Some of the square inserts give 4, but others only two (more of a diamond shape than a true square). Not sure on this last but I think that I saw that some can also be flipped over doubling the number of fresh cutting edges.
I also use HSS, as even an 11" lathe is on the small side to get the full benefit from carbide. I use the carbide on tougher materials that will dull HSS quickly.
I'm not sure if there is a big thread of inserts, but you may want to start a separate thread on selecting insert tooling. You will get more replies from people who know their carbide tools that may not see this buried in a thread about buying a lathe.