So basically when I go to start my vette in the morning, it cranks and runs fine. Later, however, after ive driven it a bit and got it warm, when i go to crank it again, it will take longer than usual to catch and run. sometimes it will also spew blue smoke out of the exhaust for a minute or so before clearing up. The other day, i drove it for about 25 mins on the highway at 70-80 mph, and later when i went to crank it again, it did what i described above, but it also seemed to want to sputter out on me until i gave it gas and drove it, and then it was fine afterwards. Not sure what can cause that, or if its just a normal thing that carburetors do, or what.
This specific car was garage kept by the old owner, but he didnt drive it much, he only cranked it every once in a while. I'm unsure if this is just something thats being caused because of it sitting, or if something is wrong with the carb, fuel system, or if it just needs to be driven more to "bring it back around" as some would say.

I'm new to carburetors and especially new to C3 corvettes, so i have no clue how they behave normally. The carburetor i have on my vette is a Holley.
Also, when i drive it for a while and the engine gets really warm, when i am idling for a while, i can just barely hear what sounds to me like a grinding noise. it is super subtle and seems to come and go as the engine idles. Is that just a normal noise? or is it something i should be concerned about?

 

Spewing blue smoke is never normal. Carbureted engines are not really any different in use than modern injected engines. Their differences come about with starting and tuning.

That it doesn't happen first thing after sitting over night is curious and seems to lead away from sloppy valve guides. Since it happens when warm/hot, I'm thinking maybe your intake manifold gasket is allowing oil to be pulled from the lifter valley -- which gets a lot of oil flow during use.

You could try retorquing each manifold bolt and seeing if they feel loose — 30 ft-lbs following this pattern when cold:

 

A check of each spark plug may indicate which cylinder(s) is most affected by the oil. Pull them all and arrange them in the same sequence to how they come out of the engine.
Like this:

 

The puff of blue smoke could also be valve guide seals. This is not usual for a car that sits for long periods of time with only an occasional start up. As mentioned above, this is most noticeable upon start up first thing on a cold engine. Replacing valve seals not a big deal, replacing guides is a big deal as the heads must come off and go to an automotive machine shop. Jerry

 

Let's start with the grinding noise. Is this an automatic?
Sometimes the flex plate cover works its way loose and rubs on anything in the way. It has a tin sound to it. It's held on by four small bolts.
Next.
I think you should remove the fuel bowls from the Holley and spray what you can with Gumout Carb cleaner. I don't know your skill level as to how far you want to dive into this carb cleaning project. But fuel bowl removal is easy on the 4150 series anyway.
Spray the bowls, needle & seat, jets, power valve. All accessible while the main body is still bolted on the Intake.
Put it back together with new metering block gaskets & bowl gaskets.

I suspect yrs of Ethanol have gummed-up the works.