Whilst flying into Inverness looks attractive on paper it is a very small airport with limited flights/routes/airlines and hence it might not be as good an option as it seems to try to fly to there from the USA - The limited airline/connection opportunities may very well mean a significantly more expensive/longer flight than to Glasgow/Edinburgh and hence rather outweigh any benefits of flying to Inverness in the first place. It depends to some extent on where exactly you're starting from, so still worth looking into, but not automatically the best option. Inverness airport does have plenty flights to London, so it may be of more use at the end of your visit to Scotland.
Inverness in itself is a nice enough place, but its quite small and I wouldn't necessarily spend time there given how short your visit is. It's more of a staging point and transport hub for parts of the Highlands.
I'm not sure I agree that the train south is that scenic, maybe the first 60-90mins are relatively scenic (not mind blowing) and then pretty avg imo. From Inverness it's a bit more scenic for 2-3 hours more, but that journey takes about 8 hours so would eat up a lot of your limited time. If you're going from city centre to city centre then the train is competitive with the plane, but if you're starting out in the countryside with a car or in the Highlands then flying may fit better. As mentioned the overnight sleeper trains may be a good option to maximise time (www.sleeper.scot).
Daytrips from Edinburgh - If you're going to relatively nearby places like Stirling or St Andrews then that's fine (although these are easily done by public transport), but if you're talking about many of the well known places in the Highlands then if you look at a map you'll see many of them are simply a fairly long way away from Edinburgh and hence not that great for a day trip, particularly in late October when the days are getting shorter and it's getting dark earlier. Given your short time this may be the only option, but it's a long time in a car/bus. I wouldn't personally hire a car and have it in Edinburgh either - The city can be quite congested and it can be difficult to drive/park with all the narrow/one-way streets, bus lanes, tram lines etc.
I guess you need to work out what you want to see and take it from there, but you have a very short time so don't try to see too much. Many people who've not been here before grossly underestimate the size of the country and how much time it takes to get from place to place (esp in the Highlands) and try to pack in far, far too much. From what you say the best option may be to fly in to Glasgow/Edinburgh dependent on final destination (or Inverness if decent flights are available), get a car and head straight into the countryside.